We usually say that a function f is increasing at x=c if f’(c)>0. but then there’s this guy’s definition.
#question about increasing at a point
dusky eagle
But these two notions conflict with eachother
Take f(x)=x^3 at x=0
By the first definition f is not increasing at x=0
However by the second definition f is increasing at x=0
So which is right? Which one of these is the standard definition that everyone uses?
grizzled orbit
By the first definition f is not increasing at x=0
Can you explain why?
dusky eagle
f’(x)=3x^2
f’(0)=0
0 is not > 0
grizzled orbit
That's an inflection point, f"(0)=0 too
f'(c)=0 doesn't just mean max or min at that point
grizzled orbit
That has nothing to do with what I’m asking tho
When you get both f'(x) and f"(x)=0, you are supposed to check neighborhood to find out the behavior of function
grizzled orbit
My question is what does it mean for a function to be increasing at a point
The explaination he gave is right and as you said about f'(c)>0 , that is for strictly increasing function. An increasing function is increasing at x=c if f'(c)>= 0
dusky eagle
I see