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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §13.4 Directional Derivatives and Gradients, #33 · Multivariable Calculus · Gradient & optimization

Figure A shows level curves of

Figure A shows level curves of $z = f (x, y)$ .
(a) Estimate the direction and length of grad $f$ at $P, Q, R$ .
(b) Locate two points where grad $f$ is parallel to $i + j$ .
(c) Where is $∣ grad f ∣$ largest? Where is it smallest?
(d) What is your estimate of $z_{m a x}$ on this figure?
(e) On the straight line from $P$ to $R$ , describe $z$ and estimate its maximum.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §13.4 Directional Derivatives and Gradients, #33

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