Question

Find the average rate of f(x) = (1/2) X^2 - 3 from 1 to 4.

Answer 1

The average rate of change of f(x) between 1 and 4 is computed as follows:

`(f(4)-f(1))/(4-1)`

f(x) evaluated at x = 4 and x = 1 are computed as follows:

`\begin{gathered} f(x)=(1)/(2)x^2-3 \\ f(4)=(1)/(2)4^2-3=5 \\ f(1)=(1)/(2)1^2-3=-(5)/(2) \end{gathered}`

Then, the average rate of change is:

`(5-(-(5)/(2)))/(4-1)=((15)/(2))/(3)=(15)/(6)`