G12 SUPER GIO
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LEARN MISSIONpartial derivatives, gradients, multiple integrals, and optimization

partial derivatives, gradients, multiple integrals, and optimization

WORKED SOURCEWORKED SOURCE

Gradient on a hill

For f(x,y)=x^2+2y^2, grad f=<2x,4y>. At (1,-1), grad f=<2,-4>.

  1. The gradient points toward steepest increase; its magnitude is sqrt(20).
  2. Trace the worked reasoning before selecting the conclusion.

Which direction gives the greatest increase?

MODELSurface Change Viewer
MATH
PROVEChoose with evidence
CLUE

Pause. Find what matters. Then make your move.