Taking the derivative of an absolute value?

[bballvas]

Can anyone help me with this?

The function f(x) is defined as f(x) = -2(x + 2)(x - 1)^2 on the open interval (-3,3). The function g(x) is defined as the absolute value of f(x) in the open interval (-3,3).

Determine the coordinates of the relative maxima of g(x) in the open interval. Explain your reasoning.

Thanks

 

[stapel]

Hint: Look at the graph, and define a piecewise function that corresponds to g(x). Then differentiate the pieces.

Eliz.

 

[bballvas]

Thanks, I did what you suggested and got it to work. I got (-1,8) for the relative maximum which makes sense. But there's one thing that I'm a little confused about.

My piece wise funciton for g(x) = -2x^3+6x-4, x≤-2
2x^3-6x+4, x>-2
My piece wise function for g'(x)= -6x^2+6, x≤-2
6x^2-6, x>-2

We do a number line with test points to the left and right of the critical numbers. My number line looked like this:

<------------+------------+----------->
......-1.5.... -1..... 0 ......1 ......2

which showed that there's an increasing slope at -1.5 and a decreasing slope at 0 so there's a relative maximum at -1. But if I were to plug in anything less than or equal to -2 it would show that there was a decreasing slope to the left of -1 because of the piecewise function I ended up with. Is that supposed to happen?

Thanks again

 

[bballvas]

How would I show for what values of x is g'(x) not defined?

Thanks