Question

Suppose $f$is a function whose derivative $f$is given by the graph shown next. In Exercises 9–12, use the given value of $f$, an area approximation, and the Fundamental Theorem to approximate the requested value.

Given that$f\left(3\right)=2$, approximate$f\left(4\right)$.

Short answer

The approximate value is$4.125$.

Step-by-step solution

Step 1. Given Information.

Given,

Step 2. Finding the value of f(4).

Given, $f\left(3\right)=2$,

The value is approximated as follows,

$$\begin{gathered} {\int }_3^{4}f\text{'}\left(x\right)=f\left(4\right)-f\left(3\right) \\ 2.125=f\left(4\right)-2 \\ f\left(4\right)=2.125+2 \\ f\left(4\right)\approx 4.125 \end{gathered}$$

Hence, the approximate value is$4.125$.