Is there a function f , differentiable for all real x, such that | f (x) |< 2 and f (x)f ′ (x) ≥ sin(x)?
I noticed that [f(x)*f(x)]' = 2f(x)*f'(x) = [f(x)]^2
So I tried multiplying that inequality by 2.
2f (x)f ′ (x) ≥ 2sin(x)
Then I tried integrating both sides.
[f(x)]^2 ≥...
Is there a function f , differentiable for all real x, such that | f (x) |< 2 and f (x)f ′ (x) ≥ sin(x)?I noticed that [f(x)*f(x)]' = 2f(x)*f'(x) = [f(x)]^2
So I tried multiplying that inequality by 2.
2f (x)f ′ (x) ≥ 2sin(x)
Then I tried integrating both sides.
[f(x)]^2 ≥ -2cos(x). This...