The number of mailings should the Canter send to each area of the country to get the responses it needs at least possible cost and the minimum cost where the Canter would like to poll at least 1500 democrats and 1500 republicans, each mailing to East coast gets responses from 100 democrats and 50 republicans, each mailing to Midwest gets responses from 100 democrats and 100 republicans and each mailing to West coast gets responses from 50 democrats and 100 republicans and mailings to East coast cost $ 40 each to produce and mail, mailings to Midwest cost $ 60 each to produce and mail and mailings to West coast cost $ 50 each to produce and mail.

Question

Consider the function f(x) = x²-1. (a) Find the instantaneous rate of change of f(x) at x=1 using the definition of the derivative. Show all your steps clearly. (b) Sketch the graph of f(x) around x = 1. Draw the secant line passing through the points on the graph where x 1 and x-> 1+h (for a small positive value of h, illustrate conceptually). Then, draw the tangent line to the graph at x=1. Explain how the slope of the tangent line relates to the value you found in part (a). (c) In a few sentences, explain what the instantaneous rate of change of f(x) at x = 1 represents in the context of the graph of f(x). How does the rate of change of this function vary at different points?

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Chapter 6.4, Problem 27E

To determine

To calculate: The number of mailings should the Canter send to each area of the country to get the responses it needs at least possible cost and the minimum cost where the Canter would like to poll at least 1500 democrats and 1500 republicans, each mailing to East coast gets responses from 100 democrats and 50 republicans, each mailing to Midwest gets responses from 100 democrats and 100 republicans and each mailing to West coast gets responses from 50 democrats and 100 republicans and mailings to East coast cost $40 each to produce and mail, mailings to Midwest cost $60 each to produce and mail and mailings to West coast cost $50 each to produce and mail.

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Consider the function f(x) = x²-1. (a) Find the instantaneous rate of change of f(x) at x=1 using the definition of the derivative. Show all your steps clearly. (b) Sketch the graph of f(x) around x = 1. Draw the secant line passing through the points on the graph where x 1 and x-> 1+h (for a small positive value of h, illustrate conceptually). Then, draw the tangent line to the graph at x=1. Explain how the slope of the tangent line relates to the value you found in part (a). (c) In a few sentences, explain what the instantaneous rate of change of f(x) at x = 1 represents in the context of the graph of f(x). How does the rate of change of this function vary at different points?

1. The graph of ƒ is given. Use the graph to evaluate each of the following values. If a value does not exist, state that fact. и (a) f'(-5) (b) f'(-3) (c) f'(0) (d) f'(5) 2. Find an equation of the tangent line to the graph of y = g(x) at x = 5 if g(5) = −3 and g'(5) = 4. - 3. If an equation of the tangent line to the graph of y = f(x) at the point where x 2 is y = 4x — 5, find ƒ(2) and f'(2).

Does the series converge or diverge