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University of California, Riverside

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Problem 45

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(t)=12 t-t^{3}, \quad-3 \leq t<\infty

$$

Answer

See the graph

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## Discussion

## Video Transcript

All right, so four problem 40 45 A function is given by acti, which is equal to 12. T minus three t Sorry. He's t cute. Too cute and domain of dysfunction is from negative three to infinity. Okay, Now, for part of it, all this problem when you take the directive of this function. So it gives 12 miners three t squared and we let this the real due to be zero than we have t squared is equal to four. And so t could be positive or negative too. All right, so these are our local extremes already down to and have a collective too. So to check whether these two batters are absolute extreme. Um, if we check the shape of this function, that is, then we need to find out the increase interval and decreasing Devo. So the directive is minus read. He's weird. We let this to be positive then that gives t squared smaller than T. C squared is smaller than four. So our tea will be from negative to two. Positive too. So that means on this interval already, function will be increasing and from connecting affinity to elected to union to infinity or function will be decreasing. So our grab up the function will be like this neck of two and two on from 19 infinity and connected to this sissy decreasing. And then it is increasing and it is decreasing. So from Margraff, we can definitely see dead. No, these now all these local extremes are the absolute extremes. So No, no, no are absolute. Or now them is absent, okay?