/sci/ - Science & Math

>>11396235
We have a differentiable function [math]f : X \rightarrow \mathbb{R}[/math].
As you well know, the derivative is the growth rate of the function. So if at some [math]x_0 \in X[/math] we have [math]f'(x_0)>0[/math], moving a little bit to the right would increase the value of [math]f[/math], and moving to the left would decrease the value of [math]f[/math]. If [math]f'(x_0)<0[/math], we have the opposite, and this all seems to imply that maxima and minima can only be reached in points with [math]f'(x_0)=0[/math].
Notice the "if we can move a little bit to both sides." This has a precise definition as [math]x_0[/math] being an interior point of [math]X[/math]. For example, [math]1 \in [0, 1][/math] is not an interior point, and [math]f(x)=x[/math] attains its maximum in it.

>>11177253
Thanks.
>>11177262
No.
Great job bettering the thread, tho.
>>11177441
Pretty sure everyone who's ever posted in /jp/ was told to leave /jp/ at some point in time.

Formerly >>11056713
Please ask clear, understandable questions.