(a) Explanation Given information: The function, f ( x ) = 4 x 2 − 11 x − 3 . Formula used: The derivative of the function f ( x ) at x = c is given by, f ' ( c ) = lim x → c f ( x ) − f ( c ) x − c . Explanation: As the function is f ( x ) = 4 x 2 − 11 x − 3 and x = 2 , Therefore, f ( 2 ) = 4 ( 2 ) 2 − 11 ( 2 ) − 3 . ⇒ f ( 2 ) = 16 − 22 − 3 = − 9 . By using definition of derivative, ⇒ f ' ( 2 ) = lim x → 2 f ( x ) − f ( 2 ) x − 2 (b) To determine An equation of tangent line to the graph of f ( x ) = 4 x 2 − 11 x − 3 at the point ( 2 , − 9 ) . (c) To determine To graph: The function f ( x ) = 4 x 2 − 11 x − 3 and the tangent line.

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Author: Sullivan

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Chapter 14, Problem 14CT

(a)

To determine

To calculate: The derivative of function f(x)=4x2−11x−3 at x=2.

(b)

To determine

An equation of tangent line to the graph of f(x)=4x2−11x−3 at the point (2,−9).

(c)

To determine

To graph: The function f(x)=4x2−11x−3 and the tangent line.

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Chapter 14, Problem 13CT

Chapter 14, Problem 15CT

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The derivative of function f ( x ) = 4 x 2 − 11 x − 3 at x = 2 .

Solution Summary: The author calculates the derivative of the function f(x)=4x2-11x-3 at x=2.

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To calculate: The derivative of function f(x)=4x2−11x−3 at x=2.

An equation of tangent line to the graph of f(x)=4x2−11x−3 at the point (2,−9).

To graph: The function f(x)=4x2−11x−3 and the tangent line.

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