Question

Find the abs min/max

Answer 1

\(\large f(x)=2x^3-3x^2-12x+1\) on \([-2, 3]\)

Answer 2

Do you know how to find the derivative?

Answer 3

\(f'(x)=6x^2-6x-12\)

Answer 4

Do you know that the extrema occur where the derivative is zero?

Answer 5

Because when the derivative (slope) is 0, the graph will be flat at that point, so we can check to see if a max or min occurs.

Answer 6

So set it equal to 0 and solve?
x=-2, 1?

Answer 7

Then evaluate the original function at those two points to find the values of the extrema.

Answer 8

I think you mixed up the negative sign, I get x=2, -1

Answer 9

Whoops, yea.

What is the purpose of the dot-cross chart?

Answer 10

@Alchemista @timely, extrema do not necessarily occur at zero-points for the derivative. Consider \(f(x)=x^3\). \(f'(x)=0\) when \(x=0\), but no extremum occurs there.

Answer 11

Yeah I thought we could do the second deriavtive check after

Answer 12

My point is that there's more to it than just finding the critical points. You have to carry out the derivative test for extrema.

Answer 13

Yes

Answer 14

Sorry guys, have to go take my final now ._.

Thanks for all your help :)

Answer 15

good luck

Answer 16

Good job, guys *claps*