The graph opposite gives the graphical representation $\mathscr { C } _ { f }$ in an orthogonal coordinate system of a function $f$ defined and differentiable on $\mathbb { R }$. We denote $f ^ { \prime }$ the derivative function of $f$. We are given points A with coordinates (0; 5) and B with coordinates (1; 20). Point C is the point on the curve $\mathscr { C } _ { f }$ with abscissa $-2.5$. The line (AB) is tangent to the curve $\mathscr { C } _ { f }$ at point A. Questions 1 to 3 relate to this same function $f$. We can assert that: a. $f ^ { \prime } ( - 0.5 ) = 0$ b. if $x \in ] - \infty ; - 0.5 \left[ \right.$, then $f ^ { \prime } ( x ) < 0$ c. $f ^ { \prime } ( 0 ) = 15$ d. the derivative function $f ^ { \prime }$ does not change sign on $\mathbb { R }$.
The graph opposite gives the graphical representation $\mathscr { C } _ { f }$ in an orthogonal coordinate system of a function $f$ defined and differentiable on $\mathbb { R }$.\\
We denote $f ^ { \prime }$ the derivative function of $f$. We are given points A with coordinates (0; 5) and B with coordinates (1; 20). Point C is the point on the curve $\mathscr { C } _ { f }$ with abscissa $-2.5$. The line (AB) is tangent to the curve $\mathscr { C } _ { f }$ at point A.\\
Questions 1 to 3 relate to this same function $f$.
We can assert that:\\
a. $f ^ { \prime } ( - 0.5 ) = 0$\\
b. if $x \in ] - \infty ; - 0.5 \left[ \right.$, then $f ^ { \prime } ( x ) < 0$\\
c. $f ^ { \prime } ( 0 ) = 15$\\
d. the derivative function $f ^ { \prime }$ does not change sign on $\mathbb { R }$.