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University of California, Riverside

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Problem 19

a. Find the open intervals on which the function is increasing and decreasing.

b. Identify the function's local and absolute extreme values, if any, saying where they occur.

$$

g(t)=-t^{2}-3 t+3

$$

Answer

(a) See the graph

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## Discussion

## Video Transcript

so for problem 19. Uh, we have a given function, g t. And we need we first need to find the open doubles for the increase in decreasing. Now we The thing that we need to do is just to take the derivative and check the and then at the router bigger than zero and check the check. The solution so are derivative for GT will be elected to t minus three, and we let this to be positive. Then our solution will be t smaller then 3/2 So that means from negative infinity to collective 3/2 his function will be increasing and from negative three have to infinity option will be decreasing. Okay, Now, for part B, we need to find the loco extreme values. Um Okay, So in this case, um, we draw the graph of dysfunction, which is a pro, Pablo. And it's true, we should be like something like this. And at this point, which is negative three have we can reach our absolute maximum on. Didn't notice is that this point is both absolute bath absolute extreme. And also it is a local screen. So this is our loco extreme, or we can say no co and loco and absolute extreme. Okay,

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