Question

Find the absolute maximum and absolute minimum values of the function, if they exist, over the indicated interval. When no interval is specified, use the real line f(x) = x + x / 225 ​(0​,[infinity]​).

A Absolute maximum is - 30, absolute minimum is 30
B. Absolute maximum is -30, no absolute minimum
C. No absolute maximum, absolute minimum is 30
D. There are no absolute extrema.

Answer 1

The function f(x) = x + x/225 has no absolute maximum as it grows indefinitely on the interval [0, infinity]. The absolute minimum is 0, which occurs at x = 0.

Step-by-step explanation:

To find the absolute maximum and absolute minimum values of the function f(x) = x + x/225 over the interval [0,(infinity)], we must analyze the behavior of the function as x approaches infinity since the interval's lower bound is zero. For large values of x, both terms x and x/225 increase without bound, indicating that the function does not have an absolute maximum, as it will continue to grow with larger values of x. However, at x = 0, the function's value is also 0, which represents the lowest value the function can take on the given interval, indicating that the absolute minimum is 0.