a. Identify the function's local extreme values in the given domain, and say where they occur.

b. Which of the extreme values, if any, are absolute?

c. Support your findings with a graphing calculator or computer grapher.

$$

h(x)=\frac{x^{3}}{3}-2 x^{2}+4 x, \quad 0 \leq x<\infty

$$

## Discussion

## Video Transcript

Okay, so here we have a function G FX negative. X squared minus six X minus nine on the domain connected for listen, pickled eggs, lis and infinity. Okay, so g prime of X, take the derivative. Get knighted too X minus six. And then when does she prime equals zero? That happens with X equals negative three. So slick for our local extreme verjee prime when x is less than negative three this is actually gonna be positive And then to the right is negative. So g is increasing and decreasing. Yeah, and we need to actually stop the night before her here. Okay, so we'll have a kind of a local men and negative for a local man. Negative for the plug in negative for we'LL get sixteen negative sixteen and then plus twenty four. That's going to be a nice nine. Said negative one and then we have a local max ants. Okay, negative. Three Cisco meaning or nine plus eighteen. I can't minus nine zero. Welcome back to zero. And then the absolute max is going to be zero. Okay, And that's in a current night history. Good. And so the absolute men is not going to exist because his ex ghost infinity, the function is going to minus infinity, so there's no absolute, but there is an absolute and occurs that negative three course wanting to this local Max.

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