Which of the following functions decreases in the interval $(0,1)$?

Question

The function $f(x)$ is graphed in the interval $(0,1).$ Which of the following functions decreases in the interval $(0,1)$ ?

My attempt:

The function $f(x)$ is increasing in the interval $(0,1)$. So,I think $A,D$ and $E$ are incorrect. Here, I'm stuck.If $f(x)$ is increasing in the interval $(0,1)$, is this imply $f'(x)$ is also increasing in the interval $(0,1)$ ?

Answer 1

hint

Using the graph, we can say that

$$f'(0)>1$$ and $$f'(1)<1$$

thus, $f'$ seems to decrease. The answer should be $B$.