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 admit that the function $f$ represented above is defined on $\mathbb { R }$ by $f ( x ) = ( a x + b ) \mathrm { e } ^ { x }$, where $a$ and $b$ are two real numbers and that its curve intersects the x-axis at the point with coordinates ($-0.5$; 0). We can assert that: a. $a = 10$ and $b = 5$ b. $a = 2.5$ and $b = -0.5$ c. $a = -1.5$ and $b = 5$ d. $a = 0$ and $b = 5$
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 admit that the function $f$ represented above is defined on $\mathbb { R }$ by $f ( x ) = ( a x + b ) \mathrm { e } ^ { x }$, where $a$ and $b$ are two real numbers and that its curve intersects the x-axis at the point with coordinates ($-0.5$; 0).\\
We can assert that:\\
a. $a = 10$ and $b = 5$\\
b. $a = 2.5$ and $b = -0.5$\\
c. $a = -1.5$ and $b = 5$\\
d. $a = 0$ and $b = 5$