Exam 4: Applications of the Derivative

Sketch the graph of while answering the following questions. a. What is the domain and range of ? b. What are the intercepts of ? c. What, if any, are the equation(s) of vertical asymototes of ? d. What, if any, are the local min(s) and local max(s) of ? e. What, if any, are the inflection point(s) of ? f. What, if it exists, is the equation of the horizontal asymotote of ?

Determine the intervals where is concave up and concave down. Round answers to nearest hundredth.

Using a calculator or computer, estimate the absolute extrema of on the interval . Round answer to the nearest hundredth.

Find the error in the following incorrect calculation.

Use Newton's method with x₀ = 2.3 to compute x₁ and x₂ without the use of a calculator. f(x) = x³ - 3x - 5

Using Newton's method with , determine the second iteration when approximating the root to at least six-digit accuracy of the following equation.

Find all asymptotes and extrema and sketch a graph.

Using a calculator or computer determine all critical numbers of and use the First Derivative Test to classify each as a local minimum, local maximum or neither.

Find the limit.

Find all asymptotes and extrema and sketch a graph.

Find the linear approximation at x = 0 to show that the following commonly used approximation is valid for "small" x.

Use a linear approximation to estimate

Determine the intervals where is concave up and concave down.

Given the graph of , locate the absolute extrema (if they exist) on the interval .

Find the limit.

Find the slant asymptote and graph the function and its asymptote on the same axes.

Find the linear approximation at x = 0 to show that the following commonly used approximation is valid for "small" x.

Graph and its slant asymptote on the same set of axes.

Find the intervals where the function is increasing and decreasing. Use this information to determine all local extrema.

A boy standing on a cliff is watching a boat through a telescope as it approaches the base of the cliff directly below him. If the telescope is 175 feet above water level and the boat is approaching at 15 feet per second, at what rate is the angle of the telescope changing when the boat is 175 feet away?