MediumCurve sketching

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §3.3 Second Derivatives: Bending and Acceleration, #21 · Calculus · Curve sketching

If … is an even function, the centered difference … exactly equals…

If $f (x)$ is an even function, the centered difference $[f (Δ x) - f (- Δ x)] /2Δ x$ exactly equals $f^{'} (0) = 0$ . Why?

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §3.3 Second Derivatives: Bending and Acceleration, #21

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