Question

Question 15(1 point)For f() = - 2 find the rate of change on the interval [-2,4Blank 1:

Answer 1

Given,

`f(x)=x^2-2`

At x=-2, f(x) is,

`\begin{gathered} f(-2)=(-2)^2-2 \\ =4-2 \\ =2 \end{gathered}`

At x=4, f(x) has value,

`\begin{gathered} f(4)=4^2-2 \\ =16-2 \\ =14 \end{gathered}`

The rate of change of f(x) on the interval [-2,4] is,

`\begin{gathered} (df(x))/(dx)=(f(4)-f(-2))/(4-(-2)) \\ =(14-2)/(6) \\ =(12)/(6) \\ =2 \end{gathered}`

Therefore, the rate of change of f(x) on the interval [-2,4] is 2.