Answer
The statement is FALSE.
Work Step by Step
The algebraic sign (either positive or negative) of $f'(x)$ does not determine the concavity of $f(x)$. It is the algebraic sign of $f''(x)$ that determines that. You can, however, determine the concavity of $f(x)$ by looking at the graph of $f'(x)$ and seeing when it is increasing or decreasing but that information is not given so this statement is FALSE.
Look at the graph below where the graph of $f(x)$ is in RED and the graph of $f'(x)$ is in BLUE. You can see how at x = -1 the graph of $f'(x)$ is positive but $f(x)$ is still concave down.
