Final answer:
To find f'(a) for the function f(x) = 6x^2, apply the power rule to get f'(x) = 12x, consequently f'(a) = 12a. So, the correct answer is f'(a) = 12a and f'(3) = 36.
Step-by-step explanation:
The student's question is regarding the computation of the derivative f'(a) for the function f(x) = 6x^2. To find f'(a), we must apply the power rule for derivatives, which states that if f(x) = ax^n, then f'(x) = n*ax^(n-1). Applying this rule to f(x), we get f'(x) = 2*6x^1 = 12x.
Substituting a into f'(x) gives us f'(a) = 12a. Now, if we want to find f'(3), we replace a with 3, resulting in f'(3) = 12*3 = 36. Thus, the correct answer for f'(a) is 12a, and for f'(3) the answer is 36.