Answer
-32
Work Step by Step
y = $-4x^{2}$ - 6 between x = 2 and x = 6
To find the rate of change, you have to use the rate of change formula:
$\frac{f(b)-f(a)}{b-a}$
In this problem, the starting point is at 2 and the end point is 6. Therefore, a = 2 and b = 6.
Knowing this, you can plug these numbers back into the formula.
$\frac{(-4\times 6^{2}-6) - (-4\times 2^{2}-6)}{6-2}$
= $\frac{(-4\times 36-6) - (-4\times 4-6)}{4}$
= $\frac{-150 - (-22)}{4}$
= $\frac{-128}{4}$
= -32
Therefore, the rate of change equals -32.
