MediumCurve sketching

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §3.3 Second Derivatives: Bending and Acceleration, #31 · Calculus · Curve sketching

Substitute for … and … in the centered approximation …, to get…

Substitute for $f (x + Δ x)$ and $f (x - Δ x)$ in the centered approximation $[f (x + Δ x) - f (x - Δ x)] /2Δ x$ , to get $f^{'} (x) +$ error. Find the $Δ x$ and $(Δ x)^{2}$ terms in this error. Test on $f (x) = x^{3}$ at $x = 0$ .

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §3.3 Second Derivatives: Bending and Acceleration, #31

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