Consider the following fx y 7xy2 9x2 at 1 2 In the directi

Consider the following. f(x. y) = 7xy^2 + 9x^2 at (-1, 2) In the direction u = 1/2 i + squareroot 3/2 j Find the directional derivative D_uf(x, y) of the function at the Indicated point and In the Indicated direction. D_uf(-1, 2) = 5 - 14 squareroot 3 Interpret the result as a rate of change. At the point (x, y) = (-1, 2), in the direction of u, the rate of change of the function is 5 - 14 squareroot 3 Interpret the result as a slope. The slope of the tangent line to the curve C that Is the intersection of the surface f(x, y) and the plane perpendicular to the (xy plane that contains the line through the point (x, y, f(x, y)) = (-1, 2, - 28) In the direction u is 5 - 14 squareroot 3 Consider the following. f(x, y) = In squareroot 6x^2 + 6y^2; p = (3, 4), Q = (0, 5)

Solution

All your answers are correct except the one the one which is with red cross.

Actually that\'s too correct ( idea) but calculations are wrong.

At (-1,2) value of function will be = 7(-1)4 +9= -19.

Thus the point will be (-1,2,-19).

Hope this helps!

Thank you!