MediumCurve sketching

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §3.3 Second Derivatives: Bending and Acceleration, #32 · Calculus · Curve sketching

Construct a table as in the text, showing the actual errors at…

Guess a third-order approximation $f (Δ x) \approx f (0) + f^{'} (0) Δ x + \frac{1}{2} f^{''} (0) (Δ x)^{2} +______$ . Test it on $f (x) = x^{3}$ .

Construct a table as in the text, showing the actual errors at $x = 0$ in one-sided differences, centered differences, second differences, and quadratic approximations. By hand take two values of $Δ x$ , by calculator take three, by computer take four.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §3.3 Second Derivatives: Bending and Acceleration, #32

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