Answer
$f'(a)=\lim \limits_{h \to 0}(4a+2h+1)$, which equals to $4a+1$.
$f'(-2)=4\times-2+1=-7$
Work Step by Step
The algebraic derivative of a function can be described as:
$f'(a)=\lim \limits_{h \to 0}\frac{f(a+h)-f(a)}{h}$
Here, $f(a)=2a^2+a$
By substituting, we get:
$\frac{2(a+h)^2+(a+h)-(2a^2+a)}{h}=\frac{2(a^2+2ah+h^2)+a+h-2a^2-a}{h}=\frac{2a^2+4ah+2h^2+a+h-2a^2-a}{h}=\frac{4ah+2h^2+h}{h}=4a+2h+1$
$f'(a)=\lim \limits_{h \to 0}(4a+2h+1)$, which equals to $4a+1$.
$f'(-2)=4\times-2+1=-7$
