(a) Explanation Given Information: The provided function is f ( x ) = x 2 − 4 x + 7 . Formula Used: The derivative of “ f ” at x is given by f ' ( x ) = lim h → 0 f ( x + h ) − f ( x ) h provided this limit exists where y = f ( x ) represent a function f Calculation: Consider the function, f ( x ) = x 2 − 4 x + 7 Now, compute the derivate of f ( x ) = x 2 − 4 x + 7 using the formula f ' ( x ) = lim h → 0 f ( x + h ) − f ( x ) h To compute f ( x + h ) , substitute x = x + h in the function f ( x ) = x 2 − 4 x + 7 . f ' ( x ) = lim h → 0 [ ( x + h ) 2 − 4 ( x + h ) + 7 ] − ( x 2 − 4 x + 7 ) h < (b) To determine To calculate: The slope of the tangent line to the graph of f ( x ) = x 2 − 4 x + 7 at x = 3 2 and x = 2 .

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ISBN: 9780135963173

Author: Blitzer

Publisher: PEARSON CO

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Chapter 11.4, Problem 20PE

(a)

To determine

To calculate: The derivative of the function f(x)=x2−4x+7 that is, f'(x) at x.

(b)

To determine

To calculate: The slope of the tangent line to the graph of f(x)=x2−4x+7 at x=32 and x=2.

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Chapter 11.4, Problem 19PE

Chapter 11.4, Problem 21PE

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Chapter 11 Solutions

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Ch. 11.1 - Check Point 1 Find: . Ch. 11.1 - Prob. 2CP Ch. 11.1 - Prob. 3CP Ch. 11.1 - Prob. 4CP Ch. 11.1 - Prob. 5CP Ch. 11.1 - Prob. 1CVC Ch. 11.1 - Prob. 2CVC Ch. 11.1 - Prob. 3CVC Ch. 11.1 - Fill in each blank so that the resulting statement...Ch. 11.1 - Fill in each blank so that the resulting statement...

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The derivative of the function f ( x ) = x 2 − 4 x + 7 that is, f ' ( x ) at x .

Solution Summary: The author explains how to calculate the derivative of the function f(x) = 2-4x+7.