Exam 3: Differentiation

In a test flight of the McCord Terrier, McCord Aviation's experimental VTOL (vertical takeoff and landing) aircraft, it was determined that t sec after liftoff, when the craft was operated in the vertical takeoff mode, its altitude (in feet) was . Find an expression for the craft's acceleration at time t.

Find the given limit by evaluating the derivative of a suitable function at an appropriate point.

Find the derivative by solving the implicit equation for y explicitly in terms of x.

Find the first and second derivatives of the function.

Find the differential of the function.

Find the derivative of the function.

The weekly total cost function associated with manufacturing the Pulsar 25 color console television is given by . What is the marginal average cost function ?

The volume of a spherical cancerous tumor is given by . If the radius of a tumor is estimated at 0.7 cm, with a maximum error in measurement of 0.007 cm, determine the error that might occur when the volume of the tumor is calculated. Round the answer to the nearest thousandth, if necessary. __________

Lupe deposits a sum of $5,000 into an account that pays interest at the rate of r/year compounded monthly. Her investment at the end of 10 yr is given by . Approximately how much more would Lupe's account be worth at the end of the term if her account paid 9.1%/year instead of 9%/year? 9.2%/year instead of 9%/year? 9.3%/year instead of 9%/year? (Hint: Use the differential of A to answer this questions.)

Find an equation of the tangent line to the graph of the function at the point .

Find by implicit differentiation.

Find the derivative by solving the given implicit equation for y explicitly in terms of x.

Find the point(s) on the graph of the function where the slope of the tangent line is equal to .

Find the third derivative of the function.

Find the derivative of the function.

Find an equation of the tangent line to the graph of the function at the point .

The supply equation for a certain brand of radio is given by , where p is expressed in dollars/bushel and x, the quantity demanded each year, is measured in billions of bushels. The economists are forecasting a harvest of 1.8 billion bushels for the year, with a maximum error of 15% in their forecast. Determine the corresponding maximum error in the predicted price per bushel of soybeans. Round the answer to the nearest percent.

Find the differential of the function.

Let . Find the values of x for which .

The demand equation for a certain brand of metal alloy audiocassette tape is , where x represents the number (in thousands) of ten-packs demanded each week when the unit price is $p. How fast is the quantity demanded increasing when the unit price/ten-pack is $16 and the selling price is dropping at the rate of $.15/ten-pack/week? Round your answer to the nearest integer. Hint: To find the value of x when p = 16, solve the equation for x when p = 16.