Question

What is the maximum value of the first derivative of f(x)=3x^2-x^3?

Answer 1

1) find the first derivative of f(x).
2) Treat f '(x) as a new function. Go through the necessary steps to identify the max value of f '(x), again applying the derivative. Please show y our work.

Answer 2

The first derivative I got was 6x-3x^2
The second derivative I got was 6-6x

Answer 3

Let's review: Suppose I give you function g(x) and ask you to find the max of this function. What would you do to g(x)? List the steps.

Answer 4

Find the first derivative, then the second and set it equal to 0 and solve for x.

Answer 5

I need help, I thought I knew the right way to do it but I was clearly wrong

Answer 6

Yes, IF you meant "set the first derivative = to 0."

You have found the derivative of the given function, obtaining 6x-3x^2. Now pretend that this is g(x): g(x)=6x-3x^2. Again, I ask you how to determine the max value of g(x).
Please go thru the actual steps, sharing your work.

Answer 7

I thought you set the second derivative to 0

Answer 8

g(x) = 6x-3x^2
g '(x) = ?

Set g '(x) = 0 and solve for x. Your result?

Answer 9

Actually, that's exactly what I'm asking you to do (immediately above).

Answer 10

Well I did that and got x=1 but the correct answer is x=3

Answer 11

Give me a second, please; I want to try this on paper.

Answer 12

You say you've found x=1? Are you 100% sure that "the correct answer is x=3?"

Answer 13

Try taking the derivative of 6-6x. Your result?

Answer 14

Yes. I got the answer from the answer key to this book.

Answer 15

Are you sure that the label for the answer is "x="?

Answer 16

The answer says D.
The choices where
a) 0
b) 1
c) 2
d) 3
e) 4

Answer 17

I note that none of these have labels. If you say "the answer is 3," you are speaking about the value of the first derivative of the given function.

In other words, you are to find the value of f '(x) = 6x -3x^2 at x=1. Try it, please.

Answer 18

Okay I got the right answer! Thanks!

Answer 19

so, you see, it was not correct to label the max value of the deriv. of f(x) "x=3".
Rather, the correct answer would be f '(1)=3.

Answer 20

Yeah. I got that already.

Answer 21

Glad you're making progress.

Answer 22

\[A solution and an associated plot is attached.\]