| $x$ | $-\infty$ | $-1$ | $+\infty$ |
| $f(x)$ | |||
| $-\infty$ | 0 |
We are given a function $f$, assumed to be differentiable on $\mathbb{R}$, and we denote $f^{\prime}$ its derivative function.
Below is the variation table of $f$:
\begin{tabular}{ | c | c c c | }
\hline
$x$ & $-\infty$ & $-1$ & $+\infty$ \\
\hline
$f(x)$ & & & \\
& $-\infty$ & 0 & \\
\hline
\end{tabular}
According to this variation table:\\
a. $f^{\prime}$ is positive on $\mathbb{R}$.\\
b. $f^{\prime}$ is positive on $\left.]-\infty;-1\right]$\\
c. $f^{\prime}$ is negative on $\mathbb{R}$\\
d. $f^{\prime}$ is positive on $[-1;+\infty[$