Exam 3: Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions

A farmer with 710 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle.What is the largest possible total area of the four pens?

Find the critical number(s),if any,of the function

Find the number c that satisfies the conclusion of the Mean Value Theorem on the given interval. ,

Find the most general antiderivative of the function.

Find the absolute maximum and absolute minimum values,if any,of the function on [0,25]

The graph of the first derivative of a function f is shown below.At what values of x does f have a local maximum or minimum?

The function satisfies the hypotheses of Rolle's Theorem on the interval .Find all values of c that satisfy the conclusion of the theorem.

Use Newton's method with the specified initial approximation to find ,the third approximation to the root of the given equation.(Round your answer to four decimal places.)

Determine where the graph of the function is concave upward and where it is concave downward.Also,find all inflection points of the function.

Find all the critical numbers of the function.

The sum of two positive numbers is 16.What is the smallest possible value of the sum of their squares?

Find the position function of a particle moving along a coordinate line that satisfies the given condition. ,s(1) = -1

What is the minimum vertical distance between the parabolas and ?

Find a cubic function that has a local maximum value of 115 at 1 and a local minimum value of -1,184 at 7.

What constant acceleration is required to increase the speed of a car from 20 ft/s to 45 ft/s in 4 s?

Find the point on the line that is closest to the origin.

Find the critical number(s),if any of the function

The function satisfies the hypotheses of Rolle's Theorem on the interval .Find all values of c that satisfy the conclusion of the theorem.

Use Newton's method with the specified initial approximation to find ,the third approximation to the root of the given equation.(Give your answer to four decimal places.)

Given . (a)Find the intervals on which f is increasing or decreasing. (b)Find the relative maxima and relative minima of f.