Given the function f(x) = 3 + 3x^2

Question

f(a)=

f(a+h)=  

f (a+h)−f (a)/h

Answer 1

f(a) = 3 + 3a^2

f(a+h) = 3 + 3(a+h)^2 = 3 + 3a^2 + 6ah + 3h^2

[f(a+h) - f(a)]/h = [3+ 3a^2 + 6ah + 3h^2 - 3 - 3a^2]/h = [6ah +3h^2h/h = 6a +3h

[f(a+h) - f(a)]/h = 6a +3h

limit as h approaches zero is 6a