Exam 4: Applications of Differentiation

Evaluate the limit using l'Hôpital's Rule.

Find the limit.

Find the critical number(s) of the function.

Use Newton's method to obtain an approximation to the root of to within 0.00001.Select the correct Answer

The graph of the second derivative of a function is shown.State the x-coordinates of the inflection points of

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

Evaluate the limit.

Find the limit.Select the correct Answer

An aircraft manufacturer wants to determine the best selling price for a new airplane.The company estimates that the initial cost of designing the airplane and setting up the factories in which to build it will be million dollars.The additional cost of manufacturing each plane can be modeled by the function where x is the number of aircraft produced and is the manufacturing cost, in millions of dollars.The company estimates that if it charges a price (in millions of dollars) for each plane, it will be able to sell Find the cost function.

A rectangular beam will be cut from a cylindrical log of radius inches.Suppose that the strength of a rectangular beam is proportional to the product of its width and the square of its depth.Find the dimensions of the strongest beam that can be cut from the cylindrical log.

A woman is on a lake in a rowboat located one mile form the closest point of a straight shoreline (see the figure).She wishes to get to point 8 miles along the shore from by rowing to a point between and and then walking the rest of the distance.If she can row at a speed of 3 mph and walk at a speed of 4 mph, how should she pick the point to get to as quickly as possible? How much time does she require?

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

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

Find all the critical numbers of the function.

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

Identify any transitional values of at which the basic shape of the curve changes.

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

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 $2342 over 25 years.Find the interest rate on this loan.Round the rate to one decimal place.

A particle is moving with the given data.Find the position of the particle.

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