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

and the function, which is G X, defined as X squared minus four x does war. So for part Elvis problem, we need to check the extreme that local extreme values. To do that, we first take the derivative of the function, which is to X minus four, and we let this rip him to be zero we can't solve for X, though axes to that it means G too. He's a local extreme value. But for part B, we need to identify whether this extreme value local stream batteries Absolute. Now we call that shape of this function is a rebel A and the only route is too. So the function should be looked like be like this and the domain is from one to infinity. So let's say this one. And until infinity we have the increasing function from 2 to 20. So have to will be our absolute minimum. So after is absolute or cheat you sorry. Due to its absent

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