Explanation Calculation: Obtain the first derivative f ′ ( x ) as follows. f ′ ( x ) = d d x ( 5 x 5 − 3 x 4 + 2 x 3 + 7 x 2 + 4 ) = 5 ( 5 x 4 ) − 3 ( 4 x 3 ) + 2 ( 3 x 2 ) + 7 ( 2 x ) = 25 x 4 − 12 x 3 + 6 x 2 + 14 x Thus, the value of f ′ ( x ) is f ′ ( x ) = 25 x 4 − 12 x 3 + 6 x 2 + 14 x . The function f ″ ( x ) is obtained by differentiating the function f ′ ( x ) as follows. f ″ ( x ) = d d x ( 25 x 4 − 12 x 3 + 6 x 2 + 14 x ) = 25 ( 4 x 3 ) − 12 ( 3 x 2 ) + 6 ( 2 x ) + 14 ( 1 ) = 100 x 3 − 36 x 2 + 12 x + 14 Thus, the value of f ″ ( x ) is f ″ ( x ) = 100 x 3 − 36 x 2 + 12 x + 14

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Chapter 13.3, Problem 19E

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To find: The third derivative and fourth derivative for the given function f(x)=5x5−3x4+2x3+7x2+4 .

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Chapter 13.3, Problem 18E

Chapter 13.3, Problem 20E

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The third derivative and fourth derivative for the given function f ( x ) = 5 x 5 − 3 x 4 + 2 x 3 + 7 x 2 + 4 .

Solution Summary: The author explains the third and fourth derivatives for the given function f(x).

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To find: The third derivative and fourth derivative for the given function f(x)=5x5−3x4+2x3+7x2+4 .

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Chapter 13 Solutions