Hector HernandezAssignment 7MATH262, Winter 2009due 4/8/09 at 11:59 PM.1.(1 pt) The functionfxyx4y44xy3x2y4increases most rapidly at the pointP11in the directionij.The rate of increase atPin this direction is.The rate of increase atPin the direction of the pointQ21is.The equation of the tangent line to the level curvefxy15at the pointPisx1y10.2.(1 pt) The functionfxyzx4y3y2z2z5x24x4y3zincreases most rapidly at the pointP111in the di-rectionijk.The rate of increase atPin this direction is.The rate of increase atPin the direction of the pointQ326is.The equation of the tangent plane to the level surfacefxyz14 isx1y1z10.3.(1 pt) Supposefxyxy,P44andv2ij.A. Find the gradient off.∇fijNote:Your answers should be expressions ofxandy; e.g.“3x4y”.B. Find the gradient offat the pointP.∇fPijNote: Your answers should be numbers.
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