Final answer:
To find f'(a) for the function f(x) = sqrt(16), we identify that it is a constant function. The derivative of a constant is 0, so f'(a) = 0 regardless of the value of a.
Step-by-step explanation:
The student has asked to find the derivative f'(a) where the function f(x) = sqrt(16) is a constant function. In this case, the value of a is given as 16. Since the square root of 16 is a constant value (4), the derivative of a constant is always zero, hence f'(a) = 0 no matter what the value of 'a' is.
When asked to take the derivative of a constant function like f(x) = sqrt(16), you can recall that any constant’s derivative is zero because a constant does not change and thus has no rate of change, which is what a derivative represents.
To find the derivative of f(x) = sqrt(16), we need to use the power rule for differentiation. The power rule states that if we have a function of the form f(x) = x^n, where n is a constant, then the derivative is given by f'(x) = n * x^(n-1). In this case, f(x) = sqrt(16) = 4, so the derivative f'(x) = 0 * 4^(0-1) = 0.