Final answer:
For the linear function f(x) = 7x + 5, there are no critical numbers because its derivative, f'(x) = 7, is constant and never equals zero or becomes undefined. Thus, the answer is DNE (Does Not Exist).
Step-by-step explanation:
The critical numbers of a function are the values of x at which the derivative of the function is either zero or undefined. For the given function f(x) = 7x + 5, we need to find the derivative and then solve for x when the derivative is equal to zero or undefined.
The derivative of f(x) = 7x + 5 is f'(x) = 7 since the derivative of a constant is zero and the derivative of 7x with respect to x is 7. As the derivative is a constant and never equals zero or becomes undefined, there are no critical numbers for this function. Therefore, the answer is DNE (Does Not Exist).