Best solutions to - "How do you find the average rate of..."

Yaritza Estrada

Answered question

2022-04-14

How do you find the average rate of change of

y = 9 x^{3} - 2 x^{2} + 6

between x = -4 and x = 2?

Answer & Explanation

zakos2zn1mr

Beginner2022-04-15Added 10 answers

The average rate of change of y = f(x) over an interval between 2 points (a ,f(a)) and (b ,f(b) is the slope of the secant line connecting the 2 points.
To calculate the average rate of change.
Reminder

\frac{f (b) - f (a)}{b - a}

here a=-4 and b=2

f (- 4) = 9 {(- 4)}^{3} - 2 {(- 4)}^{2} + 6 = 550

f (2) = 9 {(2)}^{3} - 2 {(2)}^{2} + 6 = 70

The average rate of change between (-4 ,550) and (2 ,70) is

\frac{70 - 550}{2 - (- 4)} = \frac{- 480}{6} = - 80

This means that the average of all the slopes of lines tangent to the graph of f(x) between (-4 ,550) and (2 ,70) is - 80.

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