Question

Sketching derivatives

Answer 1

Consider something like a parabola.

Answer 2

\[
f(x)=ax^2+bx+c\\
f'(x) = 2ax+b
\]

Answer 3

\[
f'(1)=0=2a+b
\]

Answer 4

So that means \(2a=-b\)\[
f'(x) = -bx+b
\]

Answer 5

We can just let \(c=0\).

Answer 6

We can let \(a=1\), and then \(b=-2\).