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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

User Molecule
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Final answer:

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).

User Tylerwal
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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).

User Theja
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