Answer
a) $7$
b) $7x-3$
Work Step by Step
a) Now, $ m_{\tan}=\lim_\limits{ h\to 0} \dfrac{f(1+h)-f(1)}{h}$
or, $=\lim_\limits{ h\to 0} \dfrac{[3(1+h)^2+(1+h)]-[3(1)^2+1]}{h}$
or, $=\lim_\limits{ h\to 0} \dfrac{3h^2+7h}{h}$
At $(1,4)$; $ m_{\tan}=7$
b) The equation of a line is: $ y=mx+c $
Now, $ y-4=7(x-1) \implies y=7x-3$
