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Maximum rate of increase

MediumLinear AlgebraCalculus~3m

For f(x,y)=x2y+y3f(x,y)=x^2 y + y^3, at the point (1,2)(1,2), what is the maximum rate of increase of ff over all unit directions? (to 3 decimals)

Show hints (2)+
  1. The max rate of increase equals ∥∇f∥\|\nabla f\| at the point.
  2. Build ∇f=(2xy, x2+3y2)\nabla f=(2xy,\,x^2+3y^2), evaluate at (1,2)(1,2), take its length.

Answer

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13.601 (± 0.01)

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