Answer
a) $7$
b) $ y=7x-8$
Work Step by Step
a) Now, $ m_{\tan}=\lim_\limits{ h\to 0} \dfrac{f(2+h)-f(2)}{h}$
or, $=\lim_\limits{ h\to 0} \dfrac{[2(2+h)^2-(2+h)-(2+h)]-[2(2)^2-2]}{h}$
or, $=\lim_\limits{ h\to 0} \dfrac{2h^2+7h}{h}$
At $(2,6)$; $ m_{\tan}=7$
b) The equation of a line is: $ y=mx+c $
Now, $ y-6=7(x-2) \implies y=7x-8$
