HW Supplement: Antidifferentiation 1. 5x² + √x-ex +1) dx Name 2. Find the function f(x) given that f'(x)=7e* and f(0) = 15. 19-0 mats is R'(q)=6q-2.1q² dollars 3. Yoga Central estimates that the marginal revenue derived from producing q units of its yoga per unit. Determine the revenue function associated with producing and selling the mats. What is the demand equation that relates the whole-sale unit price with the quantity demanded?

The value of a car decreases each year. The rate at which the value decreases is called depreciation and is a represented by a percentage. For Alina buys a car for $25,000, and the depreciation rate is 25%. That means that her car’s value goes down by 25% each year. The value can be represented by the function V(y)=25000(0.75)^v, where V represents the value of her car and y represents the number of years that she owns a car. Find the depreciated value of her car if she keeps it for 5 years. In other words, evaluate: V(5)=25000(0.75)^5, rounding to the proper decimal place for money.

Differentiate. F(x) = (8x + 3) F'(x)= Entor vour anrwor in the ansywer box and then click Check Answer. C.

You have been placed in charge of minimizing costs on a production line. The cost model is C=100x-12^2+3x^3. The variable x represents the level of production for the given cost. Determine the production level that minimizes the average cost. A.)  Find the marginal cost.  (Divide by x and take 1st derivative) B.)  What is the production level?

R=2x(500+34x-x^2) find the marginal revenue when x=14

Use the demand equation to write out the revenue function R(x). The demand equation is p=570e^-0.001x where p is price and x is the number of units demanded

The profit function for a pen manufacturer is given by P(x) = 790x – 0.3x², where x is the number of pens sold. Use th marginal profit function to estimate the profit obtained from selling the 501st pen. Do not include a dollar sign in your answer.

Differentiate f(x) = (3x)n() for r > 0. %3D

The approximate rate of change in the number of design patent applications received in recent years is given by the equation below, where t represents the number of years since 2000 and p represents the number of design patents (in thousands). In 2017, the number of applications for a design patent was 43,340. p'(t) = 0.01021t+2.03 Complete parts (a) and (b) below. (a) Find the function that gives the total number (in thousands) of design patent applications received in year t. p(t) = (Type an exact answer.)

Find the slope of the line tangent to the graph of f(x) = 1/(2x−3) at the point x = 1 and please explain how you found it