Answer
$f'(a)=f'(3)=22$
Equation of the tangent line is $y=22x-18$
Work Step by Step
Recall that $f'(a)=\lim\limits_{x \to a}\frac{f(x)-f(a)}{x-a}$
$\implies f'(3)=\lim\limits_{x \to 3}\frac{f(x)-f(3)}{x-3}=\lim\limits_{x \to 3}\frac{(2x^{2}+10x)-(2\times3^{2}+10\times3)}{x-3}$
$=\lim\limits_{x \to 3}\frac{(2x+16)(x-3)}{x-3}=\lim\limits_{x \to 3}(2x+16)=2\times3+16=22$
Equation of the tangent line is of the form
$y-f(a)=f'(a)(x-a)$
Knowing that $a=3$ and $f(3)=48$, we have
$y-48=22(x-3)$
$\implies y=22x-18$
