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Georgia Southern University

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Problem 42

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.

$$

f(x)=(x+1)^{2}, \quad-\infty<x \leq 0

$$

Answer

See the graph

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## Discussion

## Video Transcript

All right. So we have this function in f backs equals x X one squared in the domain and divinity Synnex listening to zero. So let's take the derivative to find our critical points. It's going to be two times X plus one. So have primal be zero when X equals negative one of a critical point and negative one. So first. So let's just go ahead and plot are critical point test half prime Well, to the left of negative one. Well, the negative into the right will be positive. So we have a and then we of course, we want to stop at zero because that's where our domain stops and so dysfunction is decreasing and then increasing up zero. And so we have a local max. So a local men and I have one Republican negative one that gives us zero. So the negative one zero local men And then if we consider this end point over here a local max, we have ah, local max it zero one. The men is going to be absolute to the absolute men. His name is one because it's the vertex of the Para Ebola. There's going to be no absolute Max because the function is going off to infinity. His ex goes to minus infinity