Find the average rate of change for the function between the given values.
-$$f ( x ) = 4 x 2 ; \text { from } 0 \text { to } \frac { 7 } { 4 }$$
A) $- \frac { 3 } { 10 }$
B) $\frac { 1 } { 3 }$
C) 7
D) 2

Question

Quizplus · Accepted Answer

The average rate of change of a function $f(x)$ between two points $x_1$ and $x_2$ is given by $\frac{f(x_2) - f(x_1)}{x_2 - x_1}$. For $f(x) = 4x^2$, from $x_1 = 0$ to $x_2 = \frac{7}{4}$, we calculate $\frac{f(\frac{7}{4}) - f(0)}{\frac{7}{4} - 0} = \frac{4(\frac{7}{4})^2 - 4(0)^2}{\frac{7}{4} - 0} = \frac{49}{4}$. Simplifying gives $7$.

Find the Average Rate of Change for the Function Between f(x)=4x2; from 0 to 74f ( x ) = 4 x 2 ; \text { from } 0 \text { to } \frac { 7 } { 4 }f(x)=4x2; from 0 to 47​

Find the Average Rate of Change for the Function Between $f ( x ) = 4 x 2 ; \text { from } 0 \text { to } \frac { 7 } { 4 }$