Find f'(x) and f''(x) when f(x) = 3x^2 +7x - 3

We know that when f(x) = x^n, f'(x) = nx^n-1       (1)

So we apply this to all components of f(x), giving 

f'(x) = 2(3x) + 7 = 6x +7

to find f''(x), we apply (1) to f'(x). Giving

f''(x) = 6