Explanation Given: Function f ( t ) = 3 t 2 + 100 Formula Used: Formulas of derivatives are as follows: d d x ( c ) = 0 , where c is a constant. d d x ( x n ) = n x n − 1 d d x { c . f ( x ) } = c . d d x f ( x ) Calculation: Function is given as, f ( t ) = 3 t 2 + 100 Derivative of the above function is calculated as, d d t f ( t ) = d d t ( 3 t 2 + 100 ) f ′ ( t ) = d d t ( 3 t 2 ) + d d t ( 100 ) f ′ ( t ) = 3 d d t ( t 2 ) + 0 f ′ ( t ) = 3 ( 2 t ) f ′ ( t ) = 6 t Now, f (

Applied Calculus, 6e WileyPLUS + Loose-leaf

6th Edition

ISBN: 9781119408901

Author: Deborah Hughes-Hallett, Andrew M. Gleason, Patti Frazer Lock, Daniel E. Flath

Publisher: Wiley (WileyPLUS Products)

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Chapter 3.1, Problem 50P

To determine

To find and explain f(t), f′(t) and relative rate of change f′(t)/f(t) at t=10,

where the quantity, Q, in tons, of material at a municipal waste site is given by the function Q=f(t)=3t2+100.

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Chapter 3.1, Problem 49P

Chapter 3.1, Problem 51P

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Applied Calculus, 6e WileyPLUS + Loose-leaf

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To find and explain f ( t ) , f ′ ( t ) and relative rate of change f ′ ( t ) / f ( t ) at t = 10 , where the quantity, Q , in tons, of material at a municipal waste site is given by the function Q = f ( t ) = 3 t 2 + 100.

Solution Summary: The author explains that the quantity of material at a municipal waste site is given by the function Q=f(t)=3t 2+100.

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To find and explain f(t), f′(t) and relative rate of change f′(t)/f(t) at t=10,

where the quantity, Q, in tons, of material at a municipal waste site is given by the function Q=f(t)=3t2+100.

Want to see the full answer?

Chapter 3 Solutions

To find and explain f ( t ) , f ′ ( t ) and relative rate of change f ′ ( t ) / f ( t ) at t = 10 , where the quantity, Q , in tons, of material at a municipal waste site is given by the function Q = f ( t ) = 3 t 2 + 100.

Solution Summary: The author explains that the quantity of material at a municipal waste site is given by the function Q=f(t)=3t 2+100.

Concept explainers

Videos

To find and explain f(t), f′(t) and relative rate of change f′(t)/f(t) at t=10, where the quantity, Q, in tons, of material at a municipal waste site is given by the function Q=f(t)=3t2+100.

Want to see the full answer?

Chapter 3 Solutions

To find and explain f(t), f′(t) and relative rate of change f′(t)/f(t) at t=10,

where the quantity, Q, in tons, of material at a municipal waste site is given by the function Q=f(t)=3t2+100.