Final answer:
The second derivative of the function f(x) = 3x⁴/7a is f''(x) = 36x²/7a.
Step-by-step explanation:
The given function is f(x) = 3x⁴/7a. To find the second derivative of this function, we need to differentiate it twice with respect to x.
First, let's find the first derivative:
f'(x) = (3/7a) * 4x³ = 12x³/7a
Now, let's find the second derivative:
f''(x) = (12/7a) * 3x² = 36x²/7a
Therefore, the second derivative of the function f(x) = 3x⁴/7a is f''(x) = 36x²/7a.