Explanation Given Information: The provided function is h ( x ) = x 2 − 4 x + 2 and the interval is [ − 2 , 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 h ( x ) = x 2 − 4 x + 2 over the interval [ − 2 , 2 ] is given by, Δ h Δ x = h ( 2 ) − h ( − 2 ) 2 − ( − 2 ) Now, substitute 2 for x in the function h ( x ) = x 2 − 4 x + 2 . h ( 2 ) = ( 2 ) 2 − 4 ( 2 ) + 2 = 4 − 8 + 2 = − 2 And, substitute − 2 for x in the function h ( x ) = x 2 − 4 x + 2 . h ( − 2 ) = ( − 2 ) 2 − 4 ( − 2 ) + 2 = 4 + 8 + 2 = 14 Substituting these values in the above equation to get the average rate of change, Δ h Δ x = h ( 2 ) − h ( − 2 ) 2 − ( − 2 ) = − 2 − 14 2 + 2 = − 16 4 = − 4 The average rate of change of the function h ( x ) = x 2 − 4 x + 2 over the interval [ − 2 , 2 ] is ( − 4 )

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ISBN: 9780357667231

Author: Larson

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Chapter 2.3, Problem 5E

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To calculate: The average rate of change of the function h(x)=x2−4x+2 over the interval [−2,2] and compare it with the instantaneous rate of change at the end points of the interval.

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Chapter 2.3, Problem 4E

Chapter 2.3, Problem 6E

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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 h ( x ) = x 2 − 4 x + 2 over the interval [ − 2 , 2 ] and compare it with the instantaneous rate of change at the end points of the interval.

Solution Summary: The author calculates the average rate of change of the function h(x) = 2-4x+2 over the interval and compares it with the instantaneous rate at the end

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To calculate: The average rate of change of the function h(x)=x2−4x+2 over the interval [−2,2] and compare it with the instantaneous rate of change at the end points of the interval.

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