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University of California, Riverside

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Problem 1

Answer the following questions about the functions whose derivatives are given:

\begin{equation}\begin{array}{l}{\text { a. What are the critical points of } f ?} \\ {\text { b. On what open intervals is } f \text { increasing or decreasing? }} \\ {\text { c. At what points, if any, does } f \text { assume local maximum and }} \\ \quad {\text { minimum values? }}\end{array}\end{equation}

\begin{equation}f^{\prime}(x)=x(x-1)\end{equation}

Answer

see the graph

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## Discussion

## Video Transcript

Okay, So for the first problem, um, we're given a function with the derivative, which is X times X minus one X minus one. So the first thing we need to do is to find a critical point. That is to let this derivative to be equal to zero, then our solution in this case album, it's very obvious. Justo, he's evil. And one or one. Okay, now the second part. What I want what I'm hoping DeVos is the act increasing or decreasing. So we just need to let this derivative to be positive and solve the inequality. So this is a parabola. We have to, uh, two zeroes. 101 This one and rebel a should be luke line should be like this. So that means when X is in 0 to 1, dysfunction is increasing. Otherwise it is decreasing. So if the the open devil for the decreasing will be a negative, you can t 20 Union 12 positive infinity now for parts. Uh, we want find a local maximum and local minimum. So that is just a function value off. I have zero and f one. These two are the local extremes.