Calculus/Differentiation/Applications of Derivatives/Exercises

Relative Extrema

Find the relative maximum(s) and minimum(s), if any, of the following functions. Template:Question-answer Template:Question-answer Template:Question-answer Template:Question-answer Template:Question-answer Template:Question-answer Template:Noprint

Absolute Extrema

Determine the absolute maximum and minimum of the following functions on the given domain Template:Question-answer

Determine Intervals of Change

Find the intervals where the following functions are increasing or decreasing Template:Question-answer

Determine Intervals of Concavity

Find the intervals where the following functions are concave up or concave down Template:Question-answer Template:Question-answer Template:Question-answer Template:Question-answer Template:Question-answer Template:Question-answer Template:Noprint

Word Problems

Question 27 figure: A sphere with radius $R=3$ and center $O$. The corners of the sphere are labeled and fitted perfectly inside the sphere.

29. A canoe is being pulled toward a dock (normal to the water) using a taut rope. The canoe is normal to the water while it is being pulled. The rope is hauled in at a constant $5\mathrm{f}\mathrm{t}/\mathrm{s}$. The dock is $5\mathrm{f}\mathrm{t}$ above the water. Answer items (a) through (b).

Graphing Functions

For each of the following, graph a function that abides by the provided characteristics Template:Question-answer

Approximation Problems

By assumption, for these problems, assume $\pi \approx 3.14$ and $e\approx 2.718$ unless stated otherwise. One may use a calculator or design a computer program, but one must indicate the method and reasoning behind every step where necessary. Template:Question-answer Template:Question-answer Template:Question-answer Template:Noprint

Advanced Understanding

45. Consider the differentiable function $f(x)$ for all $x>-2$ and continuous function $g(x)$ below, where $g(x)$ is linear for all $x\ge 1$ and differentiable for all $x\in (-2,1)\cup (1,\mathrm{\infty })$, and $f(x)$ and $g(x)$ are continuous for all $x\ge -2$.