The cost (in dollars) of producing x units of a certain commodity is C(x) = 9000 + 6x + 0.3x². (a) Find the average rate of change of C with respect to x when the production level is changed (i) from x = 100 to x = 105. Average rate of change = (ii) from -100 to x = 101. Average rate of change (b) Find the instantaneous rate of change of C with respect to x when x = 100. (This is called the marginal cost.) Instantaneous rate of change %D

Find the relative rate of change of f(x)=6x4ln(x)

F(x)=8x-2; X=2, x=3 How do I find the average rate of change and net rate

The time it takes an average athlete to swim 100 meters freestyle at age x years can be modeled as t(x) = 0.181x² - 8.463x + 147.376 seconds.† (a) Numerically estimate to the nearest tenth the rate of change of the time for a 15-year-old swimmer to swim 100 meters freestyle seconds per year (of age) (b) Determine the percentage rate of change of swim time for a 15-year-old. (Round your answer to one decimal place.) % per year (of age) (c) Is a 15-year-old swimmer's time improving or getting worse as the swimmer gets older? The ---Select--- rate of change shows that swim time is ---Select--- . The swimmer's time is ---Select---

Between the ages of 7 and 11 years, a certain boy grows 1.5 inches taller each year. At age 8, he is 50 inches tall. (a) Explain why, during this period, the function giving the height of the boy in terms of his age is linear. Since the rate of change -Select- and equals Identify the slope of this function. in/yr (b) Use a formula to express the height H of the boy as a linear function of his age A during this period. H(A) = (c) What is the initial value of the function that you found in part (b)? H(0) = , the boy's height is a linear function of time. (d) Studying a graph of the boy's height as a function of his age from birth to age 7 reveals that the graph is increasing and concave down. Does this indicate that this actual height (or length) at birth was larger or smaller than your answer to part (c)? O larger O smaller Explain your reasoning.

A water balloon of mass 890 grams is rolled on level ground with an initial velocity of 38 meters per second. As it travels, water leaks from the balloon at a rate of 255 grams per second. Assume air resistance is proportional to velocity with coefficient 6 grams per second. (a) Find the velocity of the balloon as a function of time. v(t) = (b) What is the furthest distance the balloon could travel? Total distance = meters.

The monthly sales of Sunny Electronics’ new iSun media player is given by q(t)=1,077t−64t^2 units per month, t months after its introduction. The price Sunny charges is p(t)=108−t^2 dollars per iSun, t months after introduction. Find the rate of change of monthly revenue 2 months after the introduction of the iSun.

Suppose that the demand for x units of a product is x = 9,000 – 90p where p dollars is the price per unit. Then the consumer expenditure for the product is E(p) = px = p(9,000 – 90p) = 9,000p – 90p2. What is the instantaneous rate of change of consumer expenditure with respect to price at the following values? (a) any price p | (b) p = 5 (c) p = 40

The price p (in dollars) and the demand x for a particular clock radio are related by the equation x = 3000 – 10p. (A) Express the price p in terms of the demand x, and find the domain of this function. (B) Find the revenue R(x) from the sale of x clock radios. What is the domain of R? (C) Find the marginal revenue at a production level of 2200 clock radios. (D) Interpret R'(2500) = - 200.00. ...