Find the gradient of each of these functions at the point indicated.
a) y = x^2 at (3,9)
b) y = - 4x^3 at (1,-4)
c) y = 2x^4 at (-1,2)
d) y = 6x at (2, 12)

Answers

Answer 1

Answer:

Remember that the gradient is equivalent o the derivative evaluated in one point.

And remember that if we have a function like:

f(x)  a*x^n

The derivative is:

f'(x) = n*a*x^(n - 1)

Then knowing this, let's start:

a) y = x^2

the derivative is:

y' = 2*x

And we want to evaluate this in the point (3, 9), then we just need to replace x by 3.

y'(3) = 2*3 = 6

The gradient of y = x^2 at (3, 9) is 6.

b) y = -4*x^3

The derivative is:

y' = 3*(-4*x^2) = -12*x^2

And we want to evaluate this on (1, -4), then we need to replace x by 1.

y'(1) = -12*1^2 = -12

The gradient of y = -4*x^3 at (1, -4) is -12.

c) y = 2*x^4

The derivative is:

y' = 4*2*(x^3) = 8*x^3

And we want to evaluate this on (-1, 2), then we need to replace x by -1.

y'(-1) = 8*(-1)^3 = -8

The gradient of y = 2*x^4 at the point (-1, 2) is -8

d) y = 6*x

The derivative is:

y' = 6

We can see that here we do not have any dependence on x, so the gradient will be the same for all values of x, this means that the gradient at the point (2, 12) is 6.


Related Questions

What is the equation in slope-intercept form of the line that crosses the y-axis at 6 and is perpendicular to the line represented by y= (-4/9)x+5?​

Answers

Answer:

y=(9/4)x+6

Step-by-step explanation:

If it crosses at 6 then it will be +6.  A perpendicular line has a slope that is the opposite reciprocal of your current slope.

PLEASE AM TIMED STEP BY STEP

Answers

Answer:

Here you go :)

Step-by-step explanation:

How do I find the y-intercept of a graph? ​

Answers

Answer:

the y intercept on a graph is the line that goes up and down

Step-by-step explanation:

Step-by-step explanation:

Every point on the y-axis has 0 as its x-coordinate. The y-intercept is the point of intersection of the graph and the y-axis.

To find the y-intercept, let x = 0 in the equation of the graph and solve for y. The value of y is the y-intercept.

For example, what is the y-intercept of

2x + 3y = 6

Let x = 0.

2(0) + 3y = 6

Solve for y.

3y = 6

y = 2

The y-intercept is 2.

Paula bought 8 pairs of socks. She paid $104. Two pairs of socks cost the same amount. How much did each of the others pairs of socks cost?

Answers

Answer:

The other socks cost 9$.

Step-by-step explanation:

Carlo places 6 apple slices on one side of a pan balance and 12 orange slices on the other side. Each side weighs 48 grams.

What is the weight of one apple slice? One orange slice?

Answers

Answer:

apple slice = 8 grams

orange slide = 4 grams

Step-by-step explanation:

48/6 will give you the weight of each apple slice

48/12 will give you the weight of each orange slice

To find the quotient of
8
1
3, multiply 8 by
-100
- اند
O
3.
ОО
8.

Answers

Answer: 3 hope this helped (:

Someone plz help me I will give brainliest

Answers

Answer:

275 non spectators

Step-by-step explanation:

1. Subtract

42,500 - 31,750 - 10,475 =

275

2. Get answer

275 non-spectators

Pls help me I’m stuck

Answers

Step-by-step explanation:

8 gallons        m miles

                  =

6 gallons         180 miles

               or

8-m

6-180

8gallons / 6gallons = m miles/ 180miles

Find the product of the term 3ab

Answers

I it would be 3ab • 1 = 3ab

Could someone do this real quick

Answers

Answer: x= 5/7 or x= 0.714285

Step-by-step explanation:

-2x + y = 3
what does x equal​

Answers

Answer:

Step-by-step explanation:

-2x+y=3

-2x=3-y

x=[tex]\frac{3-y}{-2}[/tex]

If £29 =500 rubles how many £ are in 1,260 give your answer to 2dp

Answers

Based on the information given, it should be noted that the value of 1260 will therefore be £73.09.

Solving equations

From the information given, it was stated that £29 =500. Therefore, the equation to solve that of 1260 will go thus:

£29 =500

£1 = 500/29

£1 = 17.24

Therefore, 1260 will be:

= 1260/17.24

= £73.09

Learn more about equations on:

https://brainly.com/question/13763238

greta has piece of cloth that is 9 yards long she cut it into pieces that are each 1\3 how many pieces does greta have now

Answers

Answer:

27

Step-by-step explanation:

9 divided by 1/3 is 27

Seven people are going to share an 84-ounce bottle of soda. How many ounces will each person get to drink? Choose the correct equation and answer for this situation. I THINK THIS IS ABOUT RASIOS SO PLS HELP

Answers

Answer:

7 ÷ 84 = 84 = 12 ounces

             _

             7

Step-by-step explanation:

The equation will be 7x = 84. Then the number of ounces will each person get to drink will be 12.

What is the linear system?

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

Seven people are going to share an 84-ounce bottle of soda.

Let x be the number of the ounces bottle of soda of each person.

Then we have the equation will be

7x = 84

 x = 84 / 7

 x = 12

Then the number of ounces will each person get to drink will be 12.

More about the linear system link is given below.

https://brainly.com/question/20379472

#SPJ2

PLEASE HELP WILL GIVE BRAINLIEST! Solve |3x – 1| = |x+1| by graphing.

Answers

it wold be (0,1) and (2,3)

Answer:

Step-by-step explanation:

A machine can make 14,400 screws in 8 hours. A second machine can make twice as many screws. What is the constant of proportionality (k) between the number of screws (y) and the number of hours (x) for the second machine?

Answers

Answer:

1800 screws per hour

Step-by-step explanation:

Please help me asap!!

Answers

Answer:

the second one ( - 3, -6)

Step-by-step explanation:

I used the method of substitution

Answer:

(-3, -6)

Step-by-step explanation:

What operation would you use to solve: x+7=10

Answers

Answer:

x=3

Step-by-step explanation:

x+7=10

x+7-7=10-7

x=3

Answer:

You would use subtraction

Step-by-step explanation:

To get 7 away, you need to subtract it

In ΔIJK, k = 59 cm, i = 80 cm and ∠J=106°. Find the length of j, to the nearest centimeter.

Answers

Answer:

112 cm.

Step-by-step explanation:

A triangle is a polygon with three sides and three angles. The types of triangles are scalene triangle, equilateral triangle, right angled triangle and obtuse triangle.

Cosine rule states that given a triangle with sides a, b, c and their corresponding angles opposite to the sides as A, B, C. Then:

[tex]a^2=b^2+c^2-2bc*cos(A)[/tex]

In triangle IJK:

We can find the length of j using cosine rule:

[tex]j^2=k^2+i^2-2ik*cos(J)\\\\substituting:\\\\j^2=59^2+80^2-2(80)(59)cos(106)\\\\j^2=3481+6400-(-2602)\\\\j^2=3481+6400+2602\\\\j^2=12483\\\\j=\sqrt{12483} \\\\j=112\ cm[/tex]

The solution to the system of equations is (-7, 11). true or false

Answers

What’s the equation?

Please help! I am pretty sure that is correct, however looking for confirmation. Thanks you

Answers

Answer:

yes you did right answer

the number of employees for a certain company had been decreasing each year by 8%. If the company currently has 860 employees and this rate continues, fund the number of employees in 19 years.

Answers

Answer:

approximately 684 employees

Step-by-step explanation:

So this is an exponential equation since there is a dividing decrease, not just subtracting. The standard equation is,

[tex]y = a(b)^{x} [/tex]. [tex]a[/tex] is initial value (860 employees) and [tex]b[/tex] is the change [tex]-8%[/tex] or [tex]0.92[/tex]. The [tex]x[/tex] would be the period of time, [tex]19[/tex]. This equation would be [tex]y = 860(0.92)^{19} [/tex].

After solving, the equation would become the following: [tex]y = 860(0.92)^{19} = 176.387242442≈176[/tex]. After subracting the number of lost employees from orginal employees ([tex]860-176=684[/tex]), we see that the company will have approximately 684 employees left after 19 years.

Which is the graph of y= 3/4x - 3?

Answers

The answer is Graph A.

The equation is written in slope-intercept form y=mx+b, so the slope m is 3/4, and the y-intercept is -3.

You can immediately eliminate graph B because its y-intercept is 3, not -3.

Then, you can count the rise/run for the other two graphs to see which one has a rise/run of 3/4. That’s graph A (graph C has a rise/run of 3/2, so it’s wrong).

A circle has radius 5 units and the equations of its two diameter are 2x-y=5 and x-3y+5=0.find the equations of the circle and show that it passes through the origin.​

Answers

Answer:

is a required equation. but I forgot to show that it passes through the origin.sorry for that.we had done in previous grade.

Darrell earns $75 per week walking dogs and cutting grass. He carns $10 more cutting grass than walking dogs. How much does Darrell
earn cutting grass?

Answers

darrell earns $85 cutting grass

What’s the X coordinate of the vertex

Answers

Step-by-step explanation:

f(x) = (x + 3)(x - 5)

In a Quadratic curve, the x-coordinate of the vertex is equidistant to the x-intercepts. (If they exist)

In f(x), our x-intercept are x = -3 and x = 5.

=> (-3 + 5)/2 = 1.

Hence the x-value of the vertex is 1.

Correct answer is x=1

Which expression is equivalent to X


Answers

Step-by-step explanation:

[tex]{( {x}^{ \frac{4}{3} } {x}^{ \frac{2}{3} })}^{ \frac{1}{3} } = {( {x}^{ \frac{4 + 2}{3} } ) }^{ \frac{1}{3} } = {( {x}^{2} ) }^{ \frac{1}{3} } \\ = {x}^{ \frac{2}{3} } [/tex]

⚠️⚠️⚠️⚠️HELLPP⚠️⚠️⚠️

Use completing the square to solve for x in the equation (x-12)(x+4)-
O x= -1 or 15
O x= 1 or 7
x=4+ JAT
O x=4573

Answers

Answer:

x = 4 ± [tex]\sqrt{73}[/tex]

Step-by-step explanation:

d it is the answer all the way at the bottom

Can someone could explain the part of simplifying rational expressions where it is x is not equal to a number. I've had a hard time understanding how to get that answer. The picture is an example in my notes.

Answers

Answer:

yeah it is bcoz if x is -1 then x+1 will be

-1+1 which is 0 and ur whole equation will say

now thats a lot of damage

3(2x + 1) = 6(5x - 4)

Answers

Answer:

X= 9 over 8 or 9/8

Step-by-step explanation:

hopefully this helps

Answer:

9/8 or 1.125 or 1 1/8

Step-by-step explanation:

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