How do you find the average rate of change of f(z)=4−3z2 from [-2,0]?

Question

zvonkurm7h · Accepted Answer

The average rate of change of f(z) 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 between the 2 points use.

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

f (0) = 4 - 3 {(0)}^{2} = 4

f (- 2) = 4 - 3 {(- 2)}^{2} = 4 - 12 = - 8

The average rate of change between (-2 ,-8) and (0 ,4) is

\frac{4 - (- 8)}{0 - (- 2)} = \frac{12}{2} = 6

This means that the average of all the slopes of lines tangent to the graph of f(z) is 6.

Raina Blackburn · Accepted Answer

Given:f(z)=4−3z2,[−2,0]The average rate of change of f(z) on the interval [a,b] is f(b)−f(a)b−aWe have that a=-2, b=0, f(z)=4−3z2Thus, f(b)−f(a)b−a=4−3(0)2−(4−3(−2)2)0−(−2)=6Answer:6

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