Set $ F'(t) = 0 $:

Mon, 04 May 2026 06:24:05 +0000

# Understanding $ F'(t) = 0 $: The Key to Finding Critical Points in Calculus When studying calculus, one of the most essential concepts is understanding derivatives and their significance in identifying critical points of a function. The equation $ F'(t) = 0 $ plays a central role in this process, marking values of the input variable $ t $ where a function $ F(t) $ has horizontal tangent slopes—and potentially local maxima, minima, or inflection points. ## What Does $ F'(t) = 0 $ Mean? The derivative $ F'(t) $ represents the instantaneous rate of change of the function $ F(t) $ with respect to $ t $. Setting $ F'(t) = 0 $ means we are searching for values of $ t $ where this rate of change is zero—indicating the function momentarily stops increasing or decreasing. Graphically, this corresponds to horizontal tangent lines on the curve of $ F(t) $.