Find the average rate of change for the function between the given values.
-$$f ( x ) = x ^ { 3 } + x ^ { 2 } - 8 x - 7 ; \text { from } 0 \text { to } 2$$
A) $- \frac { 1 } { 6 }$
B) $- 2$
C) $- 28$
D) $\frac { 1 } { 2 }$

Question

Quizplus · Accepted Answer

The average rate of change is calculated as $\frac{f(2) - f(0)}{2 - 0}$. Evaluating the function, $f(2) = 2^3 + 2^2 - 8(2) - 7 = -15$ and $f(0) = 0^3 + 0^2 - 8(0) - 7 = -7$. Thus, the average rate of change is $\frac{-15 - (-7)}{2} = \frac{-8}{2} = -4$. However, the correct choice is B, which is $-2$, indicating a mistake in the calculation or choices.

Find the Average Rate of Change for the Function Between f(x)=x3+x2−8x−7; from 0 to 2f ( x ) = x ^ { 3 } + x ^ { 2 } - 8 x - 7 ; \text { from } 0 \text { to } 2f(x)=x3+x2−8x−7; from 0 to 2

Find the Average Rate of Change for the Function Between $f ( x ) = x ^ { 3 } + x ^ { 2 } - 8 x - 7 ; \text { from } 0 \text { to } 2$