Question

If f(x) is a positive function and f'(x) > 0 for all x, show that f(x) is increasing.

Answer 1

To show that f(x) is increasing when f'(x) > 0 for all x, we can use the definition of an increasing function. A function is increasing if for any two values, x1 and x2, with x1 < x2, f(x1) < f(x2).

Step-by-step explanation:

To show that f(x) is increasing when f'(x) > 0 for all x, we can use the definition of an increasing function. A function is increasing if for any two values, x1 and x2, with x1 < x2, f(x1) < f(x2). Since f'(x) is positive for all x, it means that the slope of the function is positive everywhere. This means that as x increases, the function f(x) also increases.