MediumCurve sketching

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §3.4 Graphs, #30 · Calculus · Curve sketching

True (with reason) or false (with example)

True (with reason) or false (with example).
(a) Every ratio of polynomials has asymptotes
(b) If $f (x)$ is even so is $f^{''} (x)$
(c) If $f^{''} (x)$ is even so is $f (x)$
(d) Between vertical asymptotes, $f^{'} (x)$ touches zero.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §3.4 Graphs, #30

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