Question

Find the absolute maximum and absolute minimum values of the function f(x)=x^3-(3/2)x^2 on the interval [-1, 1]

Answer 1

Any particular method you would like to employ?

Answer 2

Well I took the derivative, which is 3x^2-3x=0, so the two critical numbers are x=0 and x=1

Answer 3

Then I put those two numbers and also the -1 and 1 into the original function to find the values

Answer 4

I came up with the values, 0, -1/2, and -5/2

Answer 5

Are those the right values?

Answer 6

Okay. Tell me why you used x = -1.

Answer 7

because I am supposed to use the numbers from the interval and enter them into the function to find the absolute max and min

Answer 8

and you have to choose the max and min from what you get out of those functions

Answer 9

Okay, that's very good following instructions. Do you know WHY you have to do that?

Answer 10

not really, I only know because my teacher taught us the rules

Answer 11

why do I have to do that

Answer 12

Well, that is a good start. Derivatives require CONTINUOUS functions and equal limits from both sides. If you cut it off, there is only one side and no derivative. You have to try such places yourself.

In this case, we got really lucky at x = 1. If we had not cut it of at x = 1, the derivative would find it. This is probably either a coincidence or a talking point for classroom discussion.

Answer 13

Ok that makes sense. so my ab. min value would be -5/2, and my ab. max. would be 0 right?

Answer 14

I would prefer the ordered pair notation. Good work!