Exam 4: Applications of Differentiation

Use the Second Derivative Test to find the relative extrema, if any, of the function Select the correct Answer

Use Newton's method to approximate the indicated root of in the interval correct to six decimal places.Use as the initial approximation.

What is the shortest possible length of the line segment that is cut off by the first quadrant and is tangent to the curve at some point? Select the correct Answer

Select the correct Answer for each question. -Evaluate the limit using l'Hôpital's Rule.

What is the function of the graph? Select the correct Answer

A skydiver leaps from a helicopter hovering high above the ground.Her velocity t sec later and before deploying her parachute is given by where is measured in meters per second.What is her terminal velocity? Hint: Evaluate

Select the correct Answer for each question. -The function satisfies the hypotheses of Rolle's Theorem on the interval Find all values of c that satisfy the conclusion of the theorem.

What can you say about point of inflation for ?

Given that the graph of f passes through the point (4, 69) and that the slope of its tangent line at is find Select the correct Answer

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

Evaluate the limit using Rule.

Find the dimensions of the rectangle enclosed in the semicircle with the largest possible area.

Use l'Hospital's Rule to calculate the exact value of the limit as

Select the correct Answer for each question. -The size of the monthly repayment that amortizes a loan of dollars in years at an interest rate of per year, compounded monthly, on the unpaid balance is given by The value of 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.

A steel pipe is being carried down a hallway 14 ft wide.At the end of the hall there is a right-angled turn into a narrower hallway 7 ft wide.What is the length of the longest pipe that can be carried horizontally around the corner?

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

A city's population (in thousands) years from now is estimated by What will the population of the city be in the long run? Hint: Find

Find the limit.

A skydiver leaps from a helicopter hovering high above the ground.Her velocity t sec later and before deploying her parachute is given by where is measured in meters per second.What is her terminal velocity? Hint: Evaluate Select the correct Answer

Find the slant asymptote of the function Select the correct Answer