(a) Explanation Given Information: The provided function is f ( x ) = 3 x 2 + x and the point is ( 1 , 4 ) . 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 ) = 3 x 2 + x and the point ( 1 , 4 ) Here, ( a , f ( a ) ) = ( 1 , 4 ) Now, compute the slope of the tangent line for the function f ( x ) = 3 x 2 + x as follows: Put a = 1 , m tan = lim h → 0 f ( 1 + h ) − f ( 1 ) h To compute f ( 1 + h ) , substitute x = 1 + h in the function f ( x ) = 3 x 2 + x . m tan = lim h → 0 [ 3 ( 1 + h ) 2 + ( 1 + h ) ] − [ 3 ( 1 ) 2 + 1 ] h Now, simplify ( 1 + h ) 2 by using the property ( A + B ) 2 = A 2 + 2 A B + B 2 . m tan = lim h → 0 [ 3 ( 1 + 2 h + h 2 ) + 1 + h ] − 4 h = lim h → 0 3 + 6 h + 3 h 2 + 1 + h − 4 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 ) = 3 x 2 + x at ( 1 , 4 ) .

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ISBN: 9780134494890

Author: Blitzer

Publisher: PEARSON

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Chapter 11.4, Problem 8PE

(a)

To determine

To calculate: The slope of the tangent line to the graph of f(x)=3x2+x at (1,4).

(b)

To determine

To calculate: The slope-intercept equation of the tangent line to the graph of f(x)=3x2+x at (1,4).

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Chapter 11.4, Problem 7PE

Chapter 11.4, Problem 9PE

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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 ) = 3 x 2 + x at ( 1 , 4 ) .

Solution Summary: The author explains how to calculate the slope of the tangent line to the graph of f(x)=3.

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To calculate: The slope of the tangent line to the graph of f(x)=3x2+x at (1,4).

To calculate: The slope-intercept equation of the tangent line to the graph of f(x)=3x2+x at (1,4).

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