Final answer:
To find h'(4), differentiate h(x) = 4 * 3f(x) to get h'(x) = 12f'(x), and then substitute the given value f '(4) = 2 to obtain h'(4) = 24.
Step-by-step explanation:
To find h'(4), we need to differentiate the given function h(x) = 4 * 3f(x). Using the constant multiple rule and chain rule of differentiation, the derivative of h(x) can be found. Since h(x) is a product of a constant and the function f(x), we can take the derivative of f(x) and then multiply by the constant.
The derivative h'(x) = 4 * 3f'(x). Substituting the given values, we get h'(4) = 4 * 3 * f'(4). We know that f'(4) = 2 from the given information. So, h'(4) = 4 * 3 * 2 = 24.