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APEX Calculus

Exercises 3.6 Review Exercises

1.

Find the extreme values of \(f(x) = {x^{2}-3x-9}\) on \([-2,3]\text{.}\)

2.

Describe the critical points of \(f(x) = \cos(x)\text{.}\)

3.

Describe the critical points of \(f(x) = \tan(x)\text{.}\)

4.

Consider \(f(x) = x^2-3x+5\) on \([-1,2]\text{;}\) find \(c\) guaranteed by the Mean Value Theorem.

5.

Consider \(f(x) = \sin(x)\) on \([-\pi/2,\pi/2]\text{;}\) find \(c\) guaranteed by the Mean Value Theorem.

6.

Use information gained from the first and second derivatives to sketch \(f(x) = \dfrac{1}{e^x+1}\text{.}\)