Explanation Given: The given quadratic function is y = f ( x ) − c . Calculation: The graph of the function y = f ( x ) is a parabola since it is a quadratic function. And the graph of y = f ( x ) − c is a vertical translation of y = f ( x ) To determine (b) To check: The function y = f ( x − c ) has a double root for a unique value of c.

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 1.2, Problem 48E

To determine

(a)

To check: The function y=f(x)−c has a double root for a unique value of c.

To determine

(b)

To check:

The function y=f(x−c) has a double root for a unique value of c.

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Chapter 1.2, Problem 47E

Chapter 1.2, Problem 49E

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(b) Find the (instantaneous) rate of change of y at x = 5. In the previous part, we found the average rate of change for several intervals of decreasing size starting at x = 5. The instantaneous rate of change of fat x = 5 is the limit of the average rate of change over the interval [x, x + h] as h approaches 0. This is given by the derivative in the following limit. lim h→0 - f(x + h) − f(x) h The first step to find this limit is to compute f(x + h). Recall that this means replacing the input variable x with the expression x + h in the rule defining f. f(x + h) = (x + h)² - 5(x+ h) = 2xh+h2_ x² + 2xh + h² 5✔ - 5 )x - 5h Step 4 - The second step for finding the derivative of fat x is to find the difference f(x + h) − f(x). - f(x + h) f(x) = = (x² x² + 2xh + h² - ])- = 2x + h² - 5h ])x-5h) - (x² - 5x) = ]) (2x + h - 5) Macbook Pro

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Chapter 1 Solutions

Calculus - Standalone book

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(a) To check: The function y = f ( x ) − c has a double root for a unique value of c.

Solution Summary: The author concludes that the function y=f(x)-c has a double root for the unique value of c.

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(a)

To check: The function y=f(x)−c has a double root for a unique value of c.

(b)

To check:

The function y=f(x−c) has a double root for a unique value of c.

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Chapter 1 Solutions

(a) To check: The function y = f ( x ) − c has a double root for a unique value of c.

Solution Summary: The author concludes that the function y=f(x)-c has a double root for the unique value of c.

Concept explainers

Videos

(a) To check: The function y=f(x)−c has a double root for a unique value of c.

(b) To check: The function y=f(x−c) has a double root for a unique value of c.

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Chapter 1 Solutions

(a)

To check: The function y=f(x)−c has a double root for a unique value of c.

(b)

To check:

The function y=f(x−c) has a double root for a unique value of c.