Final answer:
The derivative of the function f(x) = 9x + 6 is a constant 9, hence the derivative at any point, including at x = 4, x = 0, and x = -5, is 9.
Step-by-step explanation:
The function given is f(x) = 9x + 6. To find the derivatives such as f prime left parenthesis 4 right parenthesis, f prime left parenthesis 0 right parenthesis, and f prime left parenthesis negative 5 right parenthesis, we first need to differentiate the function. The derivative of 9x with respect to x is 9, and the derivative of a constant is 0. Therefore, f prime(x) = 9 for all x. This means that irrespective of the value of x, the derivative will always be 9.