Question 2 (1 point)
3
The table below gives the value of a function $f$ and its derivative $f^{\prime }$ at several values of $x$.
6
$$\text{Unknown environment 'tabular'}$$
9
Use the table to compute ${\int }_4^2{f}^{\prime }(x)dx$.
5
$-5$
1
4
7

Step 1 ：The table below gives the value of a function $f$ and its derivative $f^{\prime }$ at several values of $x$.\n\n$$\text{Unknown environment 'tabular'}$$

Step 2 ：Use the table to compute ${\int }_4^2{f}^{\prime }(x)dx$.

Step 3 ：The integral of a function's derivative from a to b is equal to the function's value at b minus the function's value at a. This is a direct application of the Fundamental Theorem of Calculus. In this case, we are asked to compute ${\int }_4^2{f}^{\prime }(x)dx$, which is equal to $f(2)-f(4)$. We can find these values from the given table.

Step 4 ：From the table, we find that $f(2)=1$ and $f(4)=-6$.

Step 5 ：Subtracting these values, we find that ${\int }_4^2{f}^{\prime }(x)dx=f(2)-f(4)=1-(-6)=7$.

Step 6 ：Final Answer: The value of ${\int }_4^2{f}^{\prime }(x)dx$ is $\boxed{{\displaystyle 7}}$.