Exam 11: Derivatives Continued

Suppose that the total cost (in dollars) for a product is given by , where x is the number of units produced. Total cost functions always increase because producing more items costs more. What then must be true of the marginal cost function ? ​

The demand functions for specialty steel products are given, where p is in dollars and q is the number of units demanded. Find the interval in which the demand is inelastic. Round your answer to two decimal places. ​ ​

Find the maximum value of y. Use a graphing utility to verify your conclusion. Round your answer to three decimal places. ​ ​

Suppose that the supply of x units of a product at price p dollars per unit is given by . Approximate the price increase associated with the number of units supplied changing from 32 to 33. Round your answer to the nearest cent. ​

Medical research has shown that between heartbeats, the pressure in the aorta of a normal adult is a function of time in seconds and can be modeled by the equation Use the derivative to find the rate at which the pressure is changing after 1.9 seconds. Round your answer to two decimal places. ​

Write the equation of the line tangent to the curve at the point . ​

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 and . Round your answer to four decimal places. ​

Assume that x and y are differentiable functions of t. Find using the given values. Round your answer to two decimal places. ​ for . ​

The pH of a solution is given by , where is the concentration of hydrogen ions (in gram atoms per liter). What is the rate of change of pH with respect to if ? Round your answer to two decimal places.

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

Find . ​ ​

Find ​ ​

Find the derivative of the following function. ​ ​ ​

Suppose the weekly demand function is and the supply function before taxation is , determine what tax per item will maximize the total tax revenue? ​

Assume that water is being purified by causing it to flow through a conical filter that has a height of 5 inches and a radius of 4 inches. If the depth of the water is decreasing at a rate of 3 inches per minute when the depth is 4 inches, at what rate is the volume of water flowing out of the filter at this instant? Round your answer to two decimal places. ​

Suppose that the number of mosquitoes N (in thousands) in a certain swampy area near a community is related to the number of pounds of insecticide x sprayed on the nesting areas according to Find the rate of change of N, with respect to x when 49 pounds of insecticide are used. Round your answer to two decimal places. ​

Find dy/dx at the given point without first solving for y. at ​

Find the derivative of the following function. ​ ​

Find the derivative of the following function. ​ ​

Find if ​