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University of California, Riverside

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Problem 25

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.

$$

f(r)=3 r^{3}+16 r

$$

Answer

See the graph

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## Discussion

## Video Transcript

Okay, so four problem 25 way have here is our which is divine to be three are huge loss 16 are get now for part A We need to take that the rift here off this function So that gives ny r squared a 16 response to we let this to be positive Now the solution will be ny r squared, eager than active 16. But this is always true and we let hard to be. Well, this is always true because R squared is always bigger. We put 20 so there are times zero times nine will be zero and zero is still bigger than 16. So that means that far is increasing on are on the real numbers now for part B. So since we conclude that the function is increasing, its always increasing on on the real numbers, so there's no extreme values

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