Question

Using calculus, find the intervals on which the function f(x)= 104−x is increasing or decreasing.

A) (−[infinity],26) increasing, (26,[infinity]) decreasing
B) (−[infinity],26) decreasing, (26,[infinity]) increasing
C) (−[infinity],10) increasing, (10,[infinity]) decreasing
D) (−[infinity],10) decreasing, (10,[infinity]) increasing

Answer 1

The derivative of f(x) = 104 - x is f'(x) = -1, meaning the function is always decreasing. There is no point at which the function increases, so all provided answer options are incorrect as they suggest a change in behavior which does not occur.

Step-by-step explanation:

To find the intervals on which the function f(x) = 104 − x is increasing or decreasing, we need to calculate its derivative and analyze the sign of the derivative. The derivative of f(x) = 104 − x with respect to x is f'(x) = -1. Since the derivative is a constant negative value, this indicates that the function is decreasing for all x. Therefore, there are no intervals on which the function is increasing.

The correct answer to which intervals the function is increasing or decreasing is: (−∞,26) decreasing, (26,∞) decreasing, as the function consistently decreases. However, this does not match any of the answer options provided, as they imply a change in the behavior of the function. Since f(x) is a linear function with a negative slope, it is always decreasing, so all provided options are incorrect.