Explanation Given information: The function, f ( x ) = 2 x 2 + 8 x . Explanation: The slope of the tangent line to the graph of f ( x ) at point P = ( c , f ( c ) ) is m tan = lim x → c f ( x ) − f ( c ) x − c The slope of the tangent line to the graph of f ( x ) = 2 x 2 + 8 x at the point ( 1 , 10 ) is m tan = lim x → 1 f ( x ) − f ( 1 ) x − 1 ⇒ m tan = lim x → 1 2 x 2 + 8 x − [ 2 ( 1 ) 2 + 8 ( 1 ) ] x − 1 ⇒ m tan = lim x → 1 2 x 2 + 8 x − 10 x − 1 ⇒ m tan = lim x → 1 2 x 2 − 2 x + 10 x − 10 x − 1 <

Pearson eText for Precalculus: Concepts Through Functions, A Right Triangle Approach to Trigonometry -- Instant Access (Pearson+)

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ISBN: 9780137399581

Author: Michael Sullivan, Michael Sullivan

Publisher: PEARSON+

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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.

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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 13, Problem 30RE

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The slope of the tangent line to the graph of f(x)=2x2+8x at the point (1,10). Graph f and the tangent line.

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Chapter 13, Problem 29RE

Chapter 13, Problem 31RE

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Chapter 13 Solutions

Pearson eText for Precalculus: Concepts Through Functions, A Right Triangle Approach to Trigonometry -- Instant Access (Pearson+)

Ch. 13.1 - Graph f( x )={ 3x2ifx2 3ifx=2 (pp.100-102)Ch. 13.1 - If f( x )={ xifx0 1ifx0 what is f( 0 ) ?...Ch. 13.1 - 3. The limit of a function f (x) as x approaches c...Ch. 13.1 - If a function f has no limit as x approaches c,...Ch. 13.1 - True or False may be described by saving that the...Ch. 13.1 - True or False lim xc f( x ) exists and equals some...Ch. 13.1 - Ch. 13.1 - lim x3 ( 2 x 2 +1 )Ch. 13.1 - Ch. 13.1 - lim x0 2x x 2 +4

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The slope of the tangent line to the graph of f ( x ) = 2 x 2 + 8 x at the point ( 1 , 10 ) . Graph f and the tangent line.

Solution Summary: The author explains how to determine the slope of the tangent line to the graph of f(x) = 22+8x.

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The slope of the tangent line to the graph of f(x)=2x2+8x at the point (1,10). Graph f and the tangent line.

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Chapter 13 Solutions