Mathematics

Problem

Consider the function

f(x)=3x^{2}+5

. (i) Determine

f'(1)

. (ii) Hence obtain the equation of the tangent to the curve

y=f(x)

at the point where

x=1

. (iii) Interpret the numerical value of

f'(1)

with respect to the steepness of the curve at that point.