How to find extreme values of a function.
Answers
Answer:
See below
Step-by-step explanation:
Extreme values of a function are found by taking the first derivative of the function and setting it equal to 0. To determine if it's a minimum or maximum, we set the second derivative equal to 0 and determine if its positive or negative respectively.
Let's do [tex]f(x)=3x^4+2x^3-5x^2+7[/tex] as an example
By using the power rule where [tex]\frac{d}{dx}(x^n)=nx^{n-1}[/tex], then [tex]f'(x)=12x^3+6x^2-10x[/tex]
Now set [tex]f'(x)=0[/tex] and solve for [tex]x[/tex]:
[tex]0=12x^3+6x^2-10x[/tex]
[tex]0=2x(6x^2+3x-5)[/tex]
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\frac{-3\pm\sqrt{3^2-4(6)(-5)}}{2(6)}[/tex]
[tex]x=\frac{-3\pm\sqrt{9+120}}{12}[/tex]
[tex]x=\frac{-3\pm\sqrt{129}}{12}[/tex]
[tex]x=-\frac{3}{12}\pm\frac{\sqrt{129}}{12}[/tex]
[tex]x=-\frac{1}{4}\pm\frac{\sqrt{129}}{12}[/tex]
[tex]x_1=0,x_2\approx0.6965,x_3=-1.1965[/tex]
By plugging our critical points into [tex]f(x)[/tex], we can see that our extreme values are located at [tex](0,7)[/tex], [tex](0.6965,5.956)[/tex], and [tex](-1.1965,2.565)[/tex].
The second derivative would be [tex]f''(x)=36x^2+12x-10[/tex] and plugging in our critical points will tell us if they are minimums or maximums.
If [tex]f''(x)>0[/tex], it's a minimum, but if [tex]f''(x)<0[/tex], it's a maximum.
Since [tex]f''(0)=-10<0[/tex] then [tex](0,7)[/tex] is a local maximum
Since [tex]f''(0.6965)=15.822>0[/tex], then [tex](0.6965,5.956)[/tex] is a local minimum
Since [tex]f''(-1.1965)=27.18>0[/tex], then [tex](-1.1965,2.565)[/tex] is a global minimum
Therefore, the extreme values of [tex]f(x)=3x^4+2x^3-5x^2+7[/tex] are a global minimum of [tex](-1.1965,2.565)[/tex], a local minimum of [tex](0.6965,5.956)[/tex], and a local maximum of [tex](0,7)[/tex].
Hope this example helped you understand! I've attached a graph to help you visualize the extreme values and where they're located.
Related Questions
What is the answer to 3) 1 + 4x = −5 + 7x
Answers
Answer:
x = 2
Step-by-step explanation:
You subtract the one and carry it over to negative five which makes it negative 6 and it should be
4x = -6+ 7x
Subtract the 7x and carry it over to the 4x
And you should have
-3x=-6
And you divide by the negative 3 and since dividing a negative and negative gets a positive you should get this as your answer
X=2
Will give brainliest!
Answers
Answer:
[tex] \frac{1}{2} + \frac{5}{8} [/tex]
[tex] \frac{1 \times 4}{2 \times 4} + \frac{5}{8} [/tex]
[tex] \frac{4}{8} + \frac{5}{8} [/tex]
[tex] \frac{9}{8} [/tex]
[tex]1 \frac{1}{8} [/tex]
Answer:
all, but the bottom
Step-by-step explanation:
They all add up correctly but the one on the bottom makes no sense.---------------------------------------------------------------------------------------------------------------------------
Please help me and
explain how you got the answer
Answers
Answer:
x = 7°
Step-by-step explanation:
∠WST is an exterior angle of the triangle
The two interior angles (5x - 1) and (57) add up to WST ( 12x + 7) because they are the non-adjacent interior angles
Solve:
(5x - 1) + (57) = (12x + 7)
5x - 1 = 12x - 50
-1 = 7x - 50
49 = 7x
x = 7
-Chetan K
Expand & simplify 4 ( p + 3 ) + 4 ( p − 6 )
Answers
Answer:
8p -12Step-by-step explanation:
Expand & simplify 4 ( p + 3 ) + 4 ( p − 6 )
4(p + 3) +4(p - 6) =
4p + 12 + 4p - 24 =
8p -12
I need helpppp with 1-9
Answers
1. x=1 y=3
2. x=2 y=1
3. x=2 y=2
4. x=5 y=5
5. x=2 y=0
6. x=2 y=1
7. x=3 y=-1
8. x=1 y=-3
9. x=1 y=0
Tell me if you want a step by step on any of them!! I can add that if you want.
Hope this helped. :)
Ahmed invests an amount of $1200 for three years at 6%. Work out its a- Simple interest b- Total amount after three years.
Answers
Answer: In 3 years the money earned 18%. If we rounded to 20%, the interest would have been 500(0.20) or $100. Yes, $90 is reasonable.
[tex]\sqrt{x} +1=3\\[/tex]
Answers
Answer:
x = 4
Step-by-step explanation:
√x + 1 = 3
√x = 3 - 1
√x = 2
(√x)² = (2)²
x = 4
PLEASE HELP ME, THIS IS THE LAST QUESTION AND IM DONE
Answers
Answer:
B) x=square root of 32
Step-by-step explanation:
-3=2/3(2) what is the answer
Answers
When adding, you only add the numerators. The denominator stays the same (Assuming the denominators are the same number). If not, then you will have to find a common denominator first. IN this case, the denominator is already the same. Add the numerator
2/3 + 2/3 = 4/3
Note that the answer gotten is an “improper fraction”, because the numerator is greater than the denominator. Simplify.
4/3 = 3/3 + 1/3
Divide: 3/3 = 1
1 + 1/3 = 1 1/3
1 1/3 is your mixed fraction answer (4/3 for improper fraction answer)
Which value of m is a counterexample for the following statement?
If m is an odd prime number, then m + 2 is also prime.
Group of answer choices
7
3
5
9
11
Answers
Answer:
3
Step-by-step explanation:
because 3 is a prime number and 3+2=5 which is also a prime number
You are paid 3.50 for every case you deliver to a store. If you deliver fifty seven cases, what will you be paid for that delivery?
Answers
Answer:
199.50
Step-by-step explanation:
Given the 3.50 payment for every case delivered to a store:
This means that you will earn 199.50 for delivering 57 cases, because:
57 cases × 3.50 each case = 199.50
Therefore, you will be paid 199.50 for that delivery.
a.
Write the equation in slope intercept form of a line that goes through the points
(-7, 10) and (1,4). Hint: once you find m, you will need to solve for b
Answers
Answer:
y= -¾x + 19/4
Step-by-step explanation:
get gradient and substitute
The angle measurements in the diagram are represented by the following expressions.
Answers
Answer:
114 degrees
Step-by-step explanation:
6x+12=3x+63
-3x -12 -3x -12
3x=51
x=17
6(17) +12 = 114
Solve for bb.
42=42+9b
Answers
Answer:
0
Step-by-step explanation:
42=42+9b
We move all terms to the left:
42-(42+9b)=0
We add all the numbers together, and all the variables
-(9b+42)+42=0
We get rid of parentheses
-9b-42+42=0
We add all the numbers together, and all the variables
-9b=0
b=0/-9
b=0
5x=4y make x the subject
Answers
Answer:
[tex]x = \frac{4y}{5}[/tex]
Step-by-step explanation:
[tex]5x = 4y\\\rule{150}{0.5}\\\frac{5x=4y}{5}\\\\\boxed{x = \frac{4y}{5}}[/tex]
Hope this helps.
HELP 35 POINTS
State the domain and range to each of these functions and determine function or not.
Answers
Answer:
see below
Step-by-step explanation:
2.x<1, y=all real numbers
3. -1<=x<=3 -3<=y<=2
4. x= all real numbers, y>-2
5. 7<=x<5, 3<=y<1
6.x>-4, y>-1
solve for x
9 = x/12
Answers
Answer:
X=108
Step-by-step explanation:
Step-by-step explanation:
I have solved the answer in the attached image please ask if you have any query
Find the cost per roll if a bag of five lunch rolls is $2.50
Answers
[tex]\rule{300}{3}[/tex]
[tex]\text{Hi!}[/tex]
To find the cost per item (or in your case "rolls"), you will first have to divide the cost of the lunch rolls [tex](2.50)[/tex] by the amount of lunch rolls there are [tex](5)[/tex].
So in this case, it would look like
[tex] \textbf{$2.50/5} [/tex][tex]\text{$2.50 ÷ 5}[/tex][tex]\text{$2.50 / 5}[/tex][tex]\text{2.50}[/tex] ÷ [tex]\text{5}[/tex]
[tex]\text{=$0.50}[/tex]= [tex]\text{\ 0.50}[/tex]
[tex]\boxed{\$0.50{}}[/tex]
[tex]\rule{300}{3}[/tex]
What is meaning of irrational exponents.
Answers
Answer:
Here
Step-by-step explanation:
Irrational exponents are non repeating or infinite decimals while rational exponents are rational numbers. The value of an irrational exponent when calculated is approximate in nature while the value of rational exponent is exact.
what is 18 kg in grams
Answers
Answer:
18 000
Step-by-step explanation:
One kg is 1000 grams. 18 kg are 18 x 1000 = 18 0000 grams.
Solve for v.
–1 = 4v − 13
v =
Answers
Answer:
-1+13=4v
12=4v
v=3
....
.............
add 13 on both sides
-1 + 13 = 4v - 13 + 13
12 = 4v
divide by 4 on both sides
12/4 = 4v/4
v = 3
The distance around the edge of a circular pond is 88m. The radius,in meters,is?
Answers
Answer:
88/ 2π
Step-by-step explanation:
The lines represented by the equations 5y - x = 5 and y - x = 1 are
Answers
Answer:
Same line
Step-by-step explanation:
5y - x = 5 y - 1/5x = 1
5y = x + 5 y = 1/5x + 1
5y/5 = x/5 + 5/5
y = 1/5x + 1
solve pls brainliest
Answers
Answer:
c
Step-by-step explanation:
What are the names of these polygons?
a)
b)
c)
d)
can anyone help pls?
Answers
The slope of the line formed between point A and point C on the graph is 2/3
What is the slope of the line formed between point C and point E?
Answers
Answer:
B. 1/2
Step-by-step explanation:
i think
What is the value of x
Answers
Answer:
90-56= 34
good luck!
Answer:
90-56=34
Step-by-step explanation:
90 degrees minus the given amount of the other degrees will give u the answer 90-56=34
for brainly help me out
Answers
Answer:
2nd answer sounds like the best answer because the rate of change is -1.4.
Step-by-step explanation:
Plug in the equation.
Answer:
[tex]m=-\frac{7}{5}[/tex]
Step-by-step explanation:
B will be considered, "The correct answer" :)
HELLO PLEASE GIVE ME THE RIGHT ANSWER ASAP THANK YOU !
Answers
[tex]\large\underline{\sf{Solution-}}[/tex]
[tex]\textsf{Given expression;}\\[/tex]
[tex] \rm{23 = \frac{7}{9}(6x - 36) + 9 } \\ [/tex]
[tex] \rm{\longmapsto} \: 23 = \frac{(42x - 256)}{9} + 9 \\ [/tex]
[tex] \rm{\longmapsto} \: 23 = \frac{(42x - 256 + 81)}{9} \\ [/tex]
[tex] \rm{\longmapsto} \: 23 = \frac{(42x - 175)}{9} \\ [/tex]
[tex] \rm{\longmapsto} \: \frac{23}{1} = \frac{(42x - 175)}{9} \\ [/tex]
[tex]\textsf{By doing cross multiplication, we get}\\[/tex]
[tex] \rm{\longmapsto}23(9) = 1(42x - 175) \\ [/tex]
[tex] \rm{\longmapsto}207 =42x - 175\\ [/tex]
[tex]\rm{\longmapsto} \: 42x = - 175 - 207 \\ [/tex]
[tex]\rm{\longmapsto} \: 42x = - 379 \\ [/tex]
[tex]\rm \therefore \: x = - \frac{375}{42} \\ [/tex]
[tex]\textsf{Hence, the value of x will be -375/42 respectively.}\\[/tex]
[tex]\textbf{Read more:}[/tex]
[tex]\textsf{Similar Questions}[/tex]
Solve the expression and find the value of x. [tex] \frac{x…
https://brainly.com/question/25420312
if a wire of length 2 meters costs $10. find the cost of a wire of length 35cm $1.75
Answers
Answer:
$1.75Step-by-step explanation:
if a wire of length 2 meters costs $10. find the cost of a wire of length 35cm $1.75
2m = 200 cm
200 : 10 = 35 : x
x = 10 * 35 : 200
x = 1.75
