Final answer:
The critical number of the function g(x) = f(ax + b) is found by setting the derivative of f with respect to ax + b to zero, resulting in a critical point at x = -b/a assuming the derivative of f is never undefined.
Step-by-step explanation:
The critical number of g(x) = f(ax + b) can be found by first understanding what a critical number is. A critical number of a function is a point where the derivative of the function is either zero or undefined. To find the critical number for g(x), we would need to take the derivative of g(x) with respect to x, which, by the chain rule, would involve the derivative of f with respect to its argument evaluated at ax + b, multiplied by a (the derivative of ax + b with respect to x).
Therefore, if we assume that the derivative of f is never undefined, the critical number would occur where the derivative of f equals zero. Since we are interested in the argument of f, which is ax + b, we would set f'(ax + b) = 0. Solving for x, we find that the critical number is -b/a since the x that makes ax + b equals zero is -b/a.