Question

Given the function y= (kx-2)^3, where k is a constant, find the value of k such that y will have an inflection point at x= -1. Fully justify your answer.

Answer 1

@jim_thompson5910
@zepdrix

Answer 2

y= (kx-2)^3

y'= 3k(kx-2)^2 ... derive once

y''= 6k^2(kx-2) ... derive again

Now plug in x = -1 into the second derivative function and you should get y '' = 0, so you should now have

0 = 6k^2*(k*(-1) - 2)

solve for k to get your answer(s)

Answer 3

k= 0, -2?

Answer 4

correct

Answer 5

But since the problem says k is a nonzero constant, I should reject 0, so k is -2?

Answer 6

yep

Answer 7

i see "k is a constant", but if k is nonzero, then it's just k = -2

Answer 8

Oh, oops I meant to write nonzero constant in the prob.

Answer 9

i gotcha

Answer 10

Thanks a bunch. Can I ask for further assistance?

Answer 11

sure whats your question

Answer 12

I have a few actually.

Answer 13

ok how much is a few?

Answer 14

umm, 3.

Answer 15

ok go ahead

Answer 16

A homeowner wishes to create an outdoor pet area surrounded by fencing, but comprised of two sections of equal area. The homeowner would like to enclose a total area of 150 square feet and wants to know the minimum amount of fencing to purchase and what dimensions to use. A layout of the pet area is shown below. Determine the total amount of fencing needed and the outer dimensions of the area.

Answer 17

since they have a common side (call it the width W) and equal area, they must share a common length L

Answer 18

Total Amount of Fencing:

P = W+W+W + L+L+L+L

P = 3W + 4L

Answer 19

Each rectangle has an area of 75 square ft (cut 150 sq ft in half), so

LW = 75

L = 75/W

Answer 20

P = 3W + 4L

P = 3W + 4(75/W)

P = 3W + 300/W

P = 3W^2/W + 300/W

P = (3W^2 + 300)/W

So the perimeter or the total length of fencing is (3W^2 + 300)/W ft

Answer 21

Wait!

Answer 22

what?

Answer 23

I dont understand how you go from P=3W+300/W to P= 3W^2/W+ 300/W

Answer 24

3W = 3W/1

3W = (3W/1)*(W/W)

3W = (3W^2)/W

Answer 25

Oh, ok.