f(x)*f'(x)?

[tranquil flame]

f(x) is some function. f'(x) is it's derivative. When f(x)f'(x)>0, then f(x) must be positive in all intervals where f'(x) is positive. The same argument goes for negative. Since the inequality is strict, you can imply that f(x), f'(x) are always positive/negative, provided they are continuous.

[warm harness]

If the function is continuous, then the part above the x-axis is an increasing function, and if it is below the x-axis, it is a decreasing function

[daring imp]

hi

great

[tranquil flame]

If you wanna multiply two numbers such that the result is greater than 0, they must be either both positive or both negative.

And since it's strictly grater 0 (meaning >0, not ≥0) they can't be 0.

I believe there once was a .solved command