Set $ h'(x) = 0 $ to find where the slope is horizontal:

Mon, 04 May 2026 09:00:00 +0000

Understanding Set $ h'(x) = 0 $: Finding Horizontal Tangents In calculus, one of the most fundamental tasks is identifying where a function’s slope is horizontal. This occurs when the derivative $ h'(x) = 0 $, indicating that the tangent line to the function $ h(x) $ is flat—neither rising nor falling. Recognizing where $ h'(x) = 0 $ helps pinpoint critical points, which are essential for determining local maxima, minima, and points of inflection in graphing and optimization. ### What Does $ h'(x) = 0 $ Mean? The derivative $ h'(x) $ represents the rate of change (slope) of the function $ h(x) $ at any point $ x $. When $ h'(x) = 0 $, the function momentarily stops increasing or decreasing. In geometric terms, this means the tangent line at that point is horizontal.