Calculus/Differentiation/Applications of Derivatives/Solutions

Relative Extrema

Find the relative maximum(s) and minimum(s), if any, of the following functions.

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

Determine Intervals of Concavity

Find the intervals where the following functions are concave up or concave down

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).

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

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 $x\ge -2$.