Exam 3: Applications of Differentiation

The size of the monthly repayment k that amortizes a loan of A dollars in N years at an interest rate of r per year, compounded monthly, on the unpaid balance is given by The value of r can be found by performing the iteration A family secured a loan of $360,000 from a bank to finance the purchase of a house. They have agreed to repay the loan in equal monthly installments of $2476 over 25 years. Find the interest rate on this loan. Round the rate to one decimal place.

Find the smallest possible area of an isosceles triangle that is circumscribed about a circle of radius .

A right circular cylinder is inscribed in a sphere of radius . Find the largest possible surface area of such a cylinder. Round the result to the nearest hundredth.

Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem.

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

Find the maximum and minimum points of the function.

Find two positive numbers whose product is and whose sum is a minimum.

Sketch the curve. Find the equation of the slant asymptote.

Sketch the graph of the function using the curve-sketching guidelines.

Find an equation of the line through the point that cuts off the least area from the first quadrant.

The average cost of producing x units of a commodity is given by the equation . Find the marginal cost at a production level of 1,255 units.

Find the horizontal and vertical asymptotes of the graph of the function .

You are given the graph of a function f. (a) Determine the intervals on which f is increasing or decreasing. (b) Find the relative maxima and relative minima of f, if any.

If an open box is made from a metal sheet 9 in. square by cutting out identical squares from each corner an bending up the resulting flaps, determine the dimensions of the box with the largest volume that can be made.

A particle moves along a straight line with velocity function and its initial displacement is . Find its position function.

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

Find the maximum and minimum points of the function.

Find the maximum area of a rectangle that can be circumscribed about a given rectangle with length and width .

For what values of does the curve have maximum and minimum points for the given function ? Select the correct answer.

Use Newton's method to find the zero of to within 0.00001 by solving the equation using