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Georgia Southern University

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Problem 20

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)=-3 t^{2}+9 t+5

$$

Answer

$$

=\frac{3}{2}

$$

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## Discussion

## Video Transcript

All right, so we have dysfunction. This negative three square MT. It's five and protect the derivative. Well, then we're going to get nineteen, sixty plus nine. Okay? And then if we find the critical points that said she prime equals zero. So that happens when tea is three. House. Okay, so let's find our intervals are function is increasing and decreasing. Three has to start by clicking and cheap prime. But when G is gyp, when exes lesson to be had, G Prime is going to be a positive. And when X is greater than three hundred, Steve Prime's gonna be negative and so g is increasing from negative Infinity two three House and it's decreasing from we have to infinity. And then our extreme well, we have a and see so local max, where the G is changing from being increasing to decrease things that local Max of. If we plug in three halves, what did we get? Actual value of its forty seven over four and X equals three hats and that's it. There's no that, and this is actually the absolute max. So have an absolute max of forty seven over four that occurs at X equals three halves, and there's no local minima, and there's no absolute minimum

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