First Derivative Test -- from Wolfram MathWorld
mathworld.wolfram.com › FirstDerivativeTestDec 17, 2021 · Suppose f(x) is continuous at a stationary point x_0. 1. If f^'(x)>0 on an open interval extending left from x_0 and f^'(x)<0 on an open interval extending right from x_0, then f(x) has a local maximum (possibly a global maximum) at x_0. 2. If f^'(x)<0 on an open interval extending left from x_0 and f^'(x)>0 on an open interval extending right from x_0, then f(x) has a local minimum (possibly ...
First derivative test - Math
https://www.math.net/first-derivative-testFirst derivative test. The first derivative test is used to examine where a function is increasing or decreasing on its domain and to identify its local maxima and minima. The first derivative is the slope of the line tangent to the graph at a given point. It may be helpful to think of the first derivative as the slope of the graph.