Given,
[tex]f(x)=x^2-2[/tex]
At x=-2, f(x) is,
[tex]\begin{gathered} f(-2)=(-2)^2-2 \\ =4-2 \\ =2 \end{gathered}[/tex]
At x=4, f(x) has value,
[tex]\begin{gathered} f(4)=4^2-2 \\ =16-2 \\ =14 \end{gathered}[/tex]
The rate of change of f(x) on the interval [-2,4] is,
[tex]\begin{gathered} \frac{df(x)}{dx}=\frac{f(4)-f(-2)}{4-(-2)} \\ =\frac{14-2}{6} \\ =\frac{12}{6} \\ =2 \end{gathered}[/tex]
Therefore, the rate of change of f(x) on the interval [-2,4] is 2.
