Exam 11: Derivatives Continued

Suppose the demand function for a product is given by where p is in hundreds of dollars and q is the number of tons. What is the elasticity of demand when the quantity demanded is 6 tons and the price is $303? Round your answer to one decimal place. ​

At what y-value does the curve defined by have a vertical tangent? ​

Suppose that the monthly revenue and cost (in dollars) for x units of a product are . At what rate per month is the profit changing if the number of units produced and sold is 100 and is increasing at a rate of 10 units per month? ​

p is the price per unit in dollars and q is the number of units. The monthly demand function is and the supply function before taxation is Find the tax per unit t that will maximize the tax revenue T.

For human beings, the surface area S of the body is related to the body's weight W according to , where k is a constant. For find the percent rate of change of the body's surface area in terms of the percent rate of change of the body's weight. ​

For selected years from 1978 to 2000, the number of mutual funds N, excluding money market funds, can be modeled by where t is the number of years past 1975. Find and interpret the rate of change of the number of mutual funds in 1995. Round your answer to one decimal places. ​

Write the equation of the line tangent to the graph of at .

p is the price per unit in dollars and q is the number of units. If the demand and supply functions for a product are , and , respectively, how many items will maximize the tax revenue? ​

p is in dollars and q is the number of units. Find the elasticity of the demand function at , and use it to determine how a price increase will affect total revenue. ​

Find dy/dx for the following equation: ​ . ​

Two boats leave the same port at the same time, with boat A traveling north at 20 knots (nautical miles per hour) and boat B traveling east at 40 knots. How fast is the distance between them changing when boat A is 4 nautical miles from port? Round your answer to two decimal places. ​

p is in dollars and q is the number of units. Suppose that the demand for a product is given by . Find the elasticity when . Round your answer to two decimal places. ​

Find for and simplify. ​

Water is flowing into a barrel in the shape of a right circular cylinder at the rate of 200 in³ per minute. If the radius of the barrel is 2 in, at what rate is the depth of the water changing when the water is 29 in deep? Round your answer to two decimal places.

Find if ​

Find dy/dx for the following equation: ​ ​

Find the relative minima, and use a graphing utility to check your results. ​ ​

Find the derivative of the following function. ​ ​ ​

p is in dollars and q is the number of units. Find the elasticity of the demand function at . Round your answer to two decimal places. ​

Assume that x, y, and z are differentiable functions of t. If find when , , , and . Round your answer to two decimal places.