Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §13.6 Maxima, Minima, and Saddle Points, #54 · Multivariable Calculus · Gradient & optimization

The gradient of … at the point … is

The gradient of $x^{2} + 2 y^{2}$ at the point $(1, 1)$ is $(2, 4)$ . Steepest descent is along the line $x = 1 - 2 s, y = 1 - 4 s$ (minus sign to go downward). Minimize $x^{2} + 2 y^{2}$ with respect to the stepsize $s$ . That locates the next point ____, where steepest descent begins again.

~11 minWritten answer · check your work with Lemma

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §13.6 Maxima, Minima, and Saddle Points, #54

Stuck? A gentle nudge

No hints for this one.

Something off?

Workspace

Your working

Check your full solution

Upload photos of your handwritten work or a PDF, and Lemma will read it and tell you whether it's right — and where it first goes wrong if not.