Explanation Given: The function, f ( x ) = x 4 − 3 x 3 + 16 x Concept Used: Power rule of derivatives, d d x ( x n ) = n x n − 1 Derivative of any constant C is zero, that is, d d x ( C ) = 0 Calculation: Consider the function, f ( x ) = x 4 − 3 x 3 + 16 x In order to find the derivatives of the function use power rule of derivatives and simplify further. On differentiating the given function with respect to x , it gives f ' ( x ) = d d x ( x 4 − 3 x 3 + 16 x ) = d d x ( x 4 ) − d d x ( 3 x 3 ) + d d x ( 16 x ) = ( 4 x 4 − 1 ) − ( 3 ⋅ 3 x 3 − 1 ) + ( 16 ⋅ 1 ) = ( 4 x 3 ) &#

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ISBN: 9781305177291

Author: James Stewart, Troy Day

Publisher: Cengage Learning

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Chapter 3.3, Problem 43E

To determine

The first and second derivatives of the function f(x)=x4−3x3+16x .

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Chapter 3.3, Problem 42E

Chapter 3.3, Problem 44E

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The first and second derivatives of the function f ( x ) = x 4 − 3 x 3 + 16 x .

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The first and second derivatives of the function f(x)=x4−3x3+16x .

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