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Georgia Southern University

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Problem 26

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.

$$

h(r)=(r+7)^{3}

$$

Answer

See the graph

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## Discussion

## Video Transcript

Okay, so here we have. Each of our is our plus seven Cubans. We take the derivative we get, three kinds are seven squared. And if we want to find our critical points for each count zero, well, that's just gonna be in our equals. Negative and every troll number line. See where functions increasing or decreasing. We have made seven will test. Yeah, it's prime. But H crime is always greater than equal to zero. So each crime is going to be positive over here and positive over here. So age is going to be increasing from minus infinity to mine seven. And it's also going to be increasing from seven to infinity, and so they're actually no local. For absolute extreme. This function just increases and the levels often and increases like that.