The image contains two mathematical exercises. Let's go through the questions from Exercise 9:

Exercise 9 Details:

This exercise is about the function $f$ defined as $f(x) = ax + b + e^{-0.1x}$ where $a$ and $b$ are constants. The function's graph, labeled $C_f$, and its tangent at a specific point are depicted.

Questions:

1. Determine the value of $b$:

   • The tangent line $T$ to the curve at a given point passes through $B(4;19)$.
   • Use the point $(4, 19)$ and the derivative $f'(x)$ to find $b$.

2. Equation of Tangent Line $T$:

   • Part a: Find the equation of the tangent line $T$.
   • Part b: Express $f'(x)$ in terms of $a$, $d$, and $e$, then find the general expression for $x$.

3. Determine the maximum of $f(x)$ on $\mathbb{R}$:

   • Analyze the first derivative to find critical points and determine if it's a maximum.

Let's start by calculating the value of $b$ using the information given:

We know that the tangent line at point $A$ (which needs the x-coordinate to be specified from the graph) has the point $(4,19)$ and a slope given by the derivative at that x-coordinate.

Would you like me to calculate $b$ using the point-slope form of the tangent line, and then proceed with the other parts? Or do you have specific coordinates for point $A$ or further instructions?