Guys am I stupid or is this website stupid?

Pretty sure its the website. If the first sentence wasn't there then I could see a way it would be false, but not if it's guaranteed to be differentiable.

Oh wait it should say "monotonously" decreasing and not just decreasing for it to have to be true.
Still a misleading question though, not really a misconception.

>>8483020
Maybe it's the wording? They might mean that decreasing = not increasing != strictly decreasing.

>>8483020
The two aren't mutually exclusive anon. You are both stupid.

>>8483027
If I say "f is decreasing on (a,b)" that does not mean "f has a net decrease from a to b" it means that at all points on (a,b), f is decreasing.

>>8483029
That's retarded.

>>8483020

The derivative may be zero in isolated points. Just like -x^3 is strictly decreasing everywhere, but it has derivative zero at 0.

f may be be monotonously decreasing and the derivative might be zero
example [eqn] -x^3[/eqn]

>>8483219
It could be stationary at more than just isolated points. The function is differentiable, not smooth.

>>8483538
*analytic, not smooth

they said decreasing, not STRICTLY decreasing. So the answer is "False"

X^2sin(1/x) + x

>>8483219
It's not decreasing at 0.

>>8483541
They also said f'<0, not f' strictly <0
Stop being a dumbass