Explanation Given: The function, f ( t ) = 2 t 4 + t 2 . Concept Used: The quotient rule of derivatives: d d x [ f ( x ) g ( x ) ] = g ( x ) ⋅ d d x f ( x ) − f ( x ) ⋅ d d x g ( x ) ( g ( x ) ) 2 Power rule of derivatives: d d x ( x n ) = n x n − 1 d d x ( e x ) = e x Calculation: In order to find the derivative of the given function, use the quotient rule of derivatives. Observe that the given function is a quotient of two functions 2 t and ( 4 + t 2 )

Bundle: Biocalculus: Calculus, Probability, And Statistics For The Life Sciences + Webassign Printed Access Card For Stewart/day's Biocalculus: Calculus For Life Sciences, 1st Edition, Multi-term

1st Edition

ISBN: 9781305779037

Author: James Stewart, Troy Day

Publisher: Cengage Learning

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Chapter 3.4, Problem 16E

To determine

The derivative of the function, f(t)=2t4+t2 .

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Chapter 3.4, Problem 15E

Chapter 3.4, Problem 17E

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Consider the graphs of y = f(x) and y = g(x) in the given diagram y= f(x). y = g(x) Evaluate (f+g)(2) -5 Determine all for which g(x) < f(x) Determine all for which f(x) +3 = g(x)

I) For what value(s) of x does g(x) = -4? Separate multiple answers with commas as needed. J) Give the interval(s) of such that g(x) > 0. Use the union symbol between multiple intervals. K) Give the interval(s) of such that g(x) <0. Use the union symbol between multiple intervals.

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Bundle: Biocalculus: Calculus, Probability, And Statistics For The Life Sciences + Webassign Printed Access Card For Stewart/day's Biocalculus: Calculus For Life Sciences, 1st Edition, Multi-term

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The derivative of the function, f ( t ) = 2 t 4 + t 2 .

Solution Summary: The author explains how to find the derivative of the given function using the quotient rule and power rule of derivatives.

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The derivative of the function, f(t)=2t4+t2 .

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Chapter 3 Solutions