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

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


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 $$ 5 \,\rm ft/s $$. The dock is $$ 5 \,\rm ft $$ 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.

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 $$x \in (-2, 1) \cup (1, \infty)$$, and $$f(x)$$ and $$g(x)$$ are continuous for all $$x\ge -2$$.