Consider a function $f$ defined and twice differentiable on $\mathbb { R }$. We call $\mathscr { C }$ its graphical representation. We denote by $f ^ { \prime \prime }$ the second derivative of $f$. The curve of $f ^ { \prime \prime }$, denoted $\mathscr { C } ^ { \prime \prime }$, is represented in the graph opposite. a. $\mathscr { C }$ admits a unique inflection point; b. $f$ is convex on the interval $[ - 1 ; 2 ]$; c. $f$ is convex on $] - \infty ; - 1 ]$ and on $[2; + \infty [$; d. $f$ is convex on $\mathbb { R }$.
Consider a function $f$ defined and twice differentiable on $\mathbb { R }$. We call $\mathscr { C }$ its graphical representation. We denote by $f ^ { \prime \prime }$ the second derivative of $f$. The curve of $f ^ { \prime \prime }$, denoted $\mathscr { C } ^ { \prime \prime }$, is represented in the graph opposite.\\
a. $\mathscr { C }$ admits a unique inflection point;\\
b. $f$ is convex on the interval $[ - 1 ; 2 ]$;\\
c. $f$ is convex on $] - \infty ; - 1 ]$ and on $[2; + \infty [$;\\
d. $f$ is convex on $\mathbb { R }$.