Final answer:
The derivative of the function f(x) = 3x⁴ - 5 at x = 0 is 0, since the derivative of 3x⁴ is 12x³ which equals 0 when x is substituted with 0.
Step-by-step explanation:
To calculate the derivative of f(x) = 3x⁴ - 5 at x = 0, we first find the general derivative of f(x) and then substitute x with 0. The derivative of a constant is 0, so the -5 in our function does not contribute to the derivative.
The derivative of 3x⁴ with respect to x is 4 × 3x³, which simplifies to 12x³. At x = 0, the derivative f'(x) = 12x³ becomes f'(0) = 12(0)³ = 0.
Therefore, the derivative of f(x) at x = 0 is 0.