Homework SourseFxyexy AFindthe equation of the plane tangent to the graph o
F(x,y)=e^(x-y)
A)Findthe equation of the plane tangent to the graph of f at p.
B) use your answer to compute the linear approximation of f at point (1.1,0.8)
C)what is the unit vector that points in the direction of the steepest incline of f at p?
A)Findthe equation of the plane tangent to the graph of f at p.
B) use your answer to compute the linear approximation of f at point (1.1,0.8)
C)what is the unit vector that points in the direction of the steepest incline of f at p?
Solution
A.Eqn of tangent f(x,y)\' = e^(x-y) == slope Depending on the point you have normal that varies so tangent slop*normal slope = -1 hence normal slope = -1/e^(x-y) equation of tanget at P = e^(x-y)*x +2e^x(y) = 4 B.Linear approximation = e^(1.1-0.8) C.The unit vector is normal to tangent plane is e^4 i + e^0.3j +2k
