Let $f(x)=ax^2+bx+1$, where $a$ and $b$ are constants. Use first principles to find $f'(x)$.

Question

Let $f(x)=ax^2+bx+1$, where $a$ and $b$ are constants. Use first principles to find $f'(x)$. Given $f'(0)=-3$ and $f'(2)=5$, find $a$ and $b$.

Accepted Answer

$f'(x)=2ax+b;\ a=2,\ b=-3$

Parameterised quadratic derivative from first principles