Question

Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f(x)=7 x+5

Answer 1

The function does not have any critical numbers.

Step-by-step explanation:

To find the critical numbers of the function, we need to find the values of x where the derivative of the function is equal to zero or undefined. In this case, the function is f(x) = 7x + 5. The derivative of f(x) is simply 7. Since 7 is a constant, it is never equal to zero and is also defined for all real numbers. Therefore, the function does not have any critical numbers. So the answer is DNE (does not exist).

Answer 2

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).