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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §3.2 Maximum and Minimum Problems, #70 · Calculus · Optimization

… has slope … at

This problem goes back to the theory.

$y = x + 2 x^{2} sin (1/ x)$ has slope $1$ at $x = 0$ . But show that $y$ is not increasing on an interval around $x = 0$ , by finding points where $d y / d x = 1 - 2 cos (1/ x) + 4 x sin (1/ x)$ is negative.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §3.2 Maximum and Minimum Problems, #70

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