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# Week 9 Problem Set A.
## Reading.
Thomas Ch. 4.1 on Extreme values of a function.
Just a short exercise set on what we covered on Tuesday. This is the last material expected on Exam 2.
**NOTE.** To help you study and check your work, many of these problems come from the relevant sections in Thomas's 12th edition textbook. Find the corresponding problem in the book, and if it is an odd numbered one, the answer is in the back of the book. Of course the numbering below need not match the actual numbering in the book, so you have to look for it.
You got this!
## Problems.
### Absolute extrema on a closed interval.
For each of the following functions defined on a closed interval, find the absolute maximum and absolute minimum values, as well as where they occur.
1. $\displaystyle f(x)=\frac{2}{3}x -5$ where $-2\le x\le 3$
2. $f(x)=x^{2}-1$ where $-1 \le x \le 2$
3. $\displaystyle f(x)= -\frac{1}{x^{2}}$ where $0.5 \le x \le 2$
4. $f(x) = -3x^{2 / 3}$ where $-1 \le x \le 1$
5. $f(x) = \sqrt{4-x^{2}}$ where $-2 \le x \le 1$
6. $f(x) = \sin(x)$ where $\displaystyle-\frac{\pi}{2}\le x\le \frac{5\pi}{6}$
7. $f(x)=\csc(x)$ where $\displaystyle\frac{\pi}{3} \le x \le \frac{2\pi}{3}$
### Finding extrema from graphs.
For each of the following, label the location where there is an absolute maximum, absolute minimum, local maximum, or local minimum.
1. ![[1 teaching/smc-fall-2023-math-7/week-9/---files/Pasted image 20231024215233.png]]
2. ![[1 teaching/smc-fall-2023-math-7/week-9/---files/Pasted image 20231024215241.png]]
3. ![[1 teaching/smc-fall-2023-math-7/week-9/---files/Pasted image 20231024215303.png]]
4. ![[1 teaching/smc-fall-2023-math-7/week-9/---files/Pasted image 20231024215310.png]]
5. ![[1 teaching/smc-fall-2023-math-7/week-9/---files/Pasted image 20231024215328.png]]
6. ![[1 teaching/smc-fall-2023-math-7/week-9/---files/Pasted image 20231024215335.png]]
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