Question

The function f is continuous on the interval [3, 11] with some of its values given in the table below. Use the data in the table to approximate f’(9).

Answer 1

Given:

The function f is continuous on the interval [3, 11].

Required:

to find the approximate value f'(9).

Explanation:

The function f(x) is continuous on [3,11].

So

$\begin{gathered} f^{\prime}(9)=\frac{f(10)-f(8)}{10-8} \\ \\ =\frac{16-10}{2} \\ \\ =\frac{6}{2} \\ \\ =3 \end{gathered}$

Final Answer:

$f^{\prime}(9)=3$