the graph of the function[The graph of the functionthe graph of the first derivative of the functionThe attached graph shows the existence of turning point but the first derivative of the graphed function is never zero anywhere within the domain of the function. What does this mean?
2026-04-03 20:51:34.1775249494
Can a function have a turning point (maxima) and yet its derivative not equal zero?
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If the derivative exists, then it must equal zero. However, a function may have a turning point at which its derivative does not exist: for example, $y = |x|$ has a local minimum at $x = 0$, but its derivative does not exist at that point.