Explanation Given Information: The provided function is f ( t ) = 3 t + 5 and the interval [ 1 , 2 ] . Formula used: The power rule for differentiation states that, d d x ( x k ) = k x k − 1 The derivative of a constant times a function is d d x [ c ⋅ f ( x ) ] = c ⋅ d d x ( f ( x ) ) The derivative of a sum/difference of terms in a function, d d x ( f ± g ) = d d x f ± d d x g According to average rate change formula, if f ( x ) be the function defined on interval [ a , b ] then, Δ y Δ x = f ( b ) − f ( a ) b − a Calculation: The average rate of change of the function f ( t ) = 3 t + 5 over the interval [ 1 , 2 ] is given by, Δ f Δ t = f ( 2 ) − f ( 1 ) 2 − 1 Substitute 2 for t function f ( t ) = 3 t + 5 . f ( 2 ) = 3 ( 2 ) + 5 = 6 + 5 = 11 And, substitute 2 for t function f ( t ) = 3 t + 5 . f ( 1 ) = 3 ( 1 ) + 5 = 3 + 5 = 8 Substituting these values in the above equation to get the average rate of change, Δ f Δ t = f ( 2 ) − f ( 1 ) 2 − 1 = 11 − 8 2 − 1 = 3 1 = 3 The average rate of change of the function f ( t ) = 3 t + 5 over the interval [ 1 , 2 ] is 3

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Chapter 2.3, Problem 3E

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To calculate: The average rate of change of the function f(t)=3t+5 over the interval [1,2] and compare it with the instantaneous rate of change at the end points of the interval.

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Chapter 2.3, Problem 2E

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CALCULUS APPLIED APPROACH >PRINT UGRADE<

Ch. 2.1 - Checkpoint 1 Worked-out solution available at...Ch. 2.1 - Checkpoint2 Worked-out solution available at...Ch. 2.1 - Checkpoint 3 Worked-out solution available at...Ch. 2.1 - Checkpoint 4 Worked-out solution available at...Ch. 2.1 - Checkpoint 5 Worked-out solution available at...Ch. 2.1 - Checkpoint 6 Worked-out solution available at...Ch. 2.1 - Checkpoint 7 Worked-out solution available at...Ch. 2.1 - In Exercises 1-4, find an equation of the line...Ch. 2.1 - In Exercises 1-4, find an equation of the line...Ch. 2.1 - In Exercises 1-4, find an equation of the line...

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The average rate of change of the function f ( t ) = 3 t + 5 over the interval [ 1 , 2 ] and compare it with the instantaneous rate of change at the end points of the interval.

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To calculate: The average rate of change of the function f(t)=3t+5 over the interval [1,2] and compare it with the instantaneous rate of change at the end points of the interval.

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