(a) Explanation Given Information: The provided function is f ( x ) = 5 x 2 and the point is ( − 2 , 20 ) . Formula Used: The slope of the tangent line at the point ( a , f ( a ) ) is computed by the formula: m tan = lim h → 0 f ( a + h ) − f ( a ) h Use the property to expand the whole square: ( A − B ) 2 = A 2 − 2 A B + B 2 . Calculation: Consider the function f ( x ) = 5 x 2 and the point ( − 2 , 20 ) Here, ( a , f ( a ) ) = ( − 2 , 20 ) Now, compute the slope of the tangent line for the function f ( x ) = 5 x 2 as follows: Put a = − 2 , m tan = lim h → 0 f ( − 2 + h ) − f ( − 2 ) h To compute f ( − 2 + h ) , substitute x = − 2 + h in the function f ( x ) = 5 x 2 . m tan = lim h → 0 [ 5 ( − 2 + h ) 2 ] − 5 ( − 2 ) 2 h Now, simplify ( − 2 + h ) 2 by using the property ( A − B ) 2 = A 2 − 2 A B + B 2 . m tan = lim h → 0 5 ( 4 − 4 h + h 2 ) − 20 h = lim h → 0 20 − 20 h + 5 h 2 − 20 h Combine the like terms in the numerator (b) To determine To calculate: The slope-intercept equation of the tangent line to the graph of f ( x ) = 5 x 2 at ( − 2 , 20 ) .

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ISBN: 9780134469140

Author: Robert F. Blitzer

Publisher: PEARSON

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Chapter 11.4, Problem 5PE

(a)

To determine

To calculate: The slope of the tangent line to the graph of f(x)=5x2 at (−2,20).

(b)

To determine

To calculate: The slope-intercept equation of the tangent line to the graph of f(x)=5x2 at (−2,20).

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Chapter 11.4, Problem 4PE

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Chapter 11 Solutions

Precalculus (6th Edition)

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 slope of the tangent line to the graph of f ( x ) = 5 x 2 at ( − 2 , 20 ) .

Solution Summary: The author calculates the slope of the tangent line to the graph of f(x)=5x

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To calculate: The slope of the tangent line to the graph of f(x)=5x2 at (−2,20).

To calculate: The slope-intercept equation of the tangent line to the graph of f(x)=5x2 at (−2,20).

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Chapter 11 Solutions