### Home > CALC > Chapter 5 > Lesson 5.4.1 > Problem5-142

5-142.

Using the graph of $f^\prime(x)$ in problem 5-141, and given that $f(0) = 2$, determine the following values.

1. $f(1)$

The area under the curve between $0$ and $1$ represents displacement (or accumulated area).
However, it is given that $f(0) = 2$, which means $f(x)$ has a starting value of $y = 2$.

$f(0)+\int_{0}^{1}f'(x)dx=\underline{ \ \ \ \ \ \ \ \ \ \ \ }$

1. $f^\prime(1)$

Notice that the graph is of $f^\prime(x)$.

1. $f(−3)$

Refer to hint in part (a).

1. $f^\prime(−2)$

Refer to hint in part (b).

1. $f^{\prime\prime}(2)$

$f^{\prime\prime}(x)$ represents the slope of $f^\prime(x)$ and you are looking at the $f^\prime(x)$ graph.