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

OLEASE HELP ASAP! i’ll mark brainlest!!

Answers

Answer:

A. 3^-2

Step-by-step explanation:

the question is 3^6/3^8

according to the law of exponents

a^n/a^m = a^n-m

for this question it will be

3^6-8 which is 3^-2

you're welcome....

What is 5 times 10 pls help me

Answers

50 because if you add 10 five times you get 50

Answer:

50

Step-by-step explanation:

something called a calculator

Given: a = 12, c = 38, find b. (Round answer to the nearest tenth.)

Answers

Answer:

24

Step-by-step explanation:

you add 12 for each letter you go up

:P ??????





“ItS ToO ShOrT”

Answers

Answer:

The answer is >.

Step-by-step explanation:

78 19/88 is bigger than 74/93 because 74/93 has way less whole numbers on its side.

Below is a table of revenue and cost, in thousands of dollars, of a business. Use the best fit line to estimate the number of months until the business is no longer profitable.

Answers

Answer: It's 18

Step-by-step explanation: i took it and got it right

Which of the following expressions is equivalent to 810 x 9?
O (800 x 9) + (10 x 9)
O (81 x 9) + (10 x 9)
O (600+ 310) x 9
O
814 x 5

Answers

Answer:

(800 x 9) + (10 x 9)

Step-by-step explanation:

Find out what 810 x 9 is:

810 x 9 = 7290

Then see which expression has the same answer. Personally I'd check all of them, but luckily the first expression is the correct one so you don't need to go through the rest (since it only asks for one correct expression):

(800 x 9) = 7200

(10 x 9) = 90

7200 + 90 = 7290

Simplify: 3[(5-2)3 + 4]

Answers

Answer:

39

Step-by-step explanation:

1. Subtract the numbers ... 3(3×3+4)

2. Multiply the numbers ... 3(9+4)

3. Add the numbers ... 3×13

4. Multiply the numbers ... 39

Question 1
Solve: 25.6 - 5y + 15. 3

Answers

Answer:

40.9 - 5y

Step-by-step explanation:

25.6 - 5y + 15.3

40.9 - 5y ## ^ combine like-terms

Enter the numerator that makes the equation true.


1 3/4 + 1 1/3 = 1 _/12 + 1 4/12


The '_' is blank.

Answers

Answer:

1 3/4

Step-by-step explanation:

First write the equation in mixed fraction form as;

1 3/4 + 1 1/3 = 1 _/12 + 1 4/12 ⇒  7/4  + 4/3 = _ + 16/12

7/4  + 4/3 = _ + 16/12

37/12 = _ + 16/12

37/12 - 16/12 = _

= 21/ 12

= 1 9/12

= 1 3/4

-18W + 14t - 7 + 4w + 2t + 6

Answers

-18w+ 4w= -14w
14t-2t=12t
-7+6= -1
Answer -14w+ 12t-1

Write a quadratic function to model the graph. Please help!!

Answers

Answer:

80 because that you need to work on

6h+(-7.3d)-13+5d-2.6h=? PLEASE HELP ASAP​

Answers

Answer:

-2.3d+3.4h-13

Step-by-step explanation:

Answer:

this is the answer -2.3d+3.4h-13

Step-by-step explanation:

I hope u got it right Have a good day

Help me with this please.
I’ll mark you as a brainliest

Answers

Answer:

y=mx+b <3 have a nice day!

Step-by-step explanation:

1+ 2/5 × 4/5 ÷ 1/2( these are fractions btw)

Answers

ANSWER : 41/25 or in simplest form 1 16/25 . it could also be 1.64 in decimal form .

Answer:

41/25 or 1  16/25

Step-by-step explanation:

1 + 2/5 x 4/5 ÷ 1/2

do multiplication first

2/5 x 4/5 = 8/15

1 + 8/25 ÷ 1 /2

do division by multiplying by the reciprocal

1 + 8/25 x 2/1

1 + 16/25 = 1  16/25

Question 7 of 25
What is the approximate value of sin C?

Answers

Answer:

-0.5

Step-by-step explanation:

Quadrilateral RSTU is similair to Quadrilateral JKLM . Which statement is NOT true ?

Answers

is there a picture?



Answer:

D is congruent to quadrilateral RSTU

Step-by-step explanation:

Can anybody help me with these questions??

Answers

Answer:

The first one yes

The second one yes they are congruent

The third one yes because when you divided 34 by 27.2(34/27.2) =1.25, 23 by 18.4 (23/18.4)=1.25 and 31 by 24.8(31/24.8)=1.25 so they are proportional.

Question 1
Which number falls between 0.92 and 0.922?
0.96
0.91
0.92
0.93
0.94
0.95
Select an Answer
A) 0.918
B)0.921
C)0.938
D)0.951

Answers

B). 921
.92, .921, .922
Just like regular counting but with decimals
B- 0.921, this would fall right in between both numbers

Here is an inequality: -2x>10.

a) Choose a value for x that would make this inequality true
10
-7
5
3
b) What is a solution to the inequality -2x≥10 but not a solution to the inequality -2x>10?
4
-6
-5
5

Answers

i’m pretty sure the answer is -7 B

Please help me. Solve by using substitution.

Answers

Answer:

y=-3x+3..........(1)

6x+2y=6

putting value of y

6x+2(-3x+3)=6

6x-6x+6=6

o=0

sorry I do not get answer

Answer:

x=1, y=0

Step-by-step explanation:

Use combining like terms to simplify the expression: 7x+2−5x+4

Answers

Answer:

2x+6

Step-by-step explanation:

add the numbers:7x+6-5x

combine the like terms:7x+6-5x

2x+6

Which side in the image corresponds to Side length T V in the pre-image? Side length U T Side length V U Side length T S Side length T V

Answers

Answer:

Answer: The side in the image that corresponds to Side length TV in the pre-image is TV

Step-by-step explanation:

Answer:

T V

Step-by-step explanation:

right on edge 2022!

The number of deer in Georgia increased by 2,300 last year. Which of the situations below, when combined with that increase, will result in a zero overall change in the amount of deer in Georgia?

Group of answer choices

The population of deer decreased by 23% per month next year.

The amount of deer decreases by 2,300 during the next year.

The amount of deer stays constant during the next year.

The number of deer increases by 2,300 next year.

Answers

Answer:

D

Step-by-step explanation:

Question 5 of 10
Rise is the horizontal change between any two points on a line.
A. True
B. False
SUBMIT

Answers

Answer:

False

Rise is the vertical change not the horizontal

Step-by-step explanation:

What is the solution of 4z + 10 = 30?
-

Answers

Answer:

z = 5

Step-by-step explanation:

You must isolate the z in this situation

What is the perimeter of the plot of the parking lot?​

Answers

Answer:

give me specfic measurments and ill give you the anwser

Step-by-step explanation:

FIND NTH TERM QUICKEST IN GETS BRAINLIEST

Answers

answer is 13 because the numbers are increasing though odd numbers that are also increasing if that makes sense.

It’s going from 4 > 9 > 16 > 25 > 36

so from 4-9 it adds 5 and from 9-16 it adds 7 and goes on so that’s it’s like

+5 > +7 > +9 > +11

sorry if it doesn’t make good sense

Please help me read the attached picture

Answers

Answer:

the second one.

Step-by-step explanation:

the sum of the interior and exterior angels are 360°

Which of the following is the value of logb(1/b^3) for any base b>0?
(1)^3b
(2)^-3
(3)1/3
(4)b/3

Answers

Answer:

number 2

Step-by-step explanation:

because i did the same exersise and this is the solution

The value of  [tex]log_b(\frac{1}{b^3})[/tex] is -3.

Option B is the correct answer.

What is an expression?

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

[tex]log_b(\frac{1}{b^3})[/tex]

This can be written as,

= [tex]log_b1 - log_bb^3[/tex]

= 0 - 3 [tex]log_bb[/tex]

= 0 - 3 x 1

= 0 - 3

= -3

Thus,

The value is -3.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ2

Simplify the algebraic expression.
4 – 10c – 8c2 + 9c – 8+ 10c2

Answers

Answer:

Assuming the missign thing between the c and 2 for 2 numbers are exponents the answer is

-4-c+2c^2

SO just combune liek terms, nothing different

Its just like adding but just ember to keep the sign

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