Chapter 1.1, Problem 24E

Find the point of diminishing returns for the function, where R is the revenue (in thousands of dollars) and x is the advertising cost (in thousands of dollars). Use a graphing utility to verify your results. R = −(1/4)x3 + 3x2 + 9,   0 ≤ x ≤ 6 (x, R) =

Differentiate the function ?(?) = −2√?35(?7− √?7 −8?8 Hence or otherwise, determine ?′(1)

Which statement best describes the effects on the graph of f(x) = 2x when f(x) is replaced by −2f(x + 3) − 5? A The graph is reflected over the y-axis, vertically compressed by a scale factor of , horizontally translated 3 units to the left, and vertically translated 5 units down. B The graph is reflected over the x-axis, vertically stretched by a scale factor of 2, horizontally translated 3 units to the left, and vertically translated 5 units down. C The graph is reflected over the x-axis, vertically stretched by a scale factor of 2, horizontally translated 3 units to the right, and vertically translated 5 units down. D The graph is reflected over the y-axis, vertically compressed by a scale factor of , horizontally translated 3 units to the left, and vertically translated 5 units up.

Which of the following statements about the function y=a(k(x-d))x+c is not true?         The value of a represents a vertical stretch/compression.   The value of d represents a horizontal translation.   The value of k represents the maximum or minimum of the function.   The value of c represents a vertical translation.

#12 Bob's bank account balance is modeled by the function f(x)=35.26(1.06)^x What was Bob's original balance?

Suppose that the revenue R, in dollars, from selling x clocks is R ( x )  = 30x. The cost C, in dollars, of selling x clocks is C ( x ) = 0.1x2 + 7x + 400. Show all your work and explain in sentences. Find the profit function, P ( x ) = R ( x ) – C ( x ). Find the profit if x =  30 clocks are sold. Interpret P (30).

The average cost to produce x video games is given by the function c=50/x+6. What is the average cost to produce 1000 games? What's the average cost for 2000 games?

Write the function defined by y=f(x),subject to the condition of the value of f(x) is 16 times the value of the square root of x.

An electric current can be represented by the function y=2cos(2π(x−0.02)), with time in x seconds. How many times does the current reach a value of 1 on the interval 0<x<5? Group of answer choices 12 6 8 10