Show that b=1, c=-16 and d=20 for the function g(x)=x3+bx2+cx+d. The graph passes through (0, 20), (-5, 0) and has a local maximum at P.

Here's the solution to your differential calculus problem:

9.1.1 Show that $b=1$, $c=-16$ and $d=20$.

Step 1: Determine $d$ and $x_P$.
The graph intersects the $y$-axis at $(0; 20)$. Substituting $x=0$ into $g(x)$:

$$g(0) = (0)^3 + b(0)^2 + c(0) + d = d$$

Therefore, $d=20$.

The graph intersects the $x$-axis at $(-5; 0)$ and at P. P is also a