Question

A function is given. Determine the average rate of change of the function between
f(x) = 2 − x^2; x = 6, x = 6 + h

Answer 1

\[f(x)=2-x^2\]
\[f'(x)={f(x+h)-f(x)\over h}\]
\[f'(6)={[2-(6+h)^2]-[2-6^2]\over h}\]\[={2-6^2+12h+h^2 -2+6^2\over h}\]\[={12h+h^2 \over h}\]\[=12+1/h\]\[=12\]

Answer 2

=-12-h