V58 Consider the upper half of the ellipsoid f(x,y) = 1- 16 64 and the point F P(-2:-15 on the level curve foxy)= 8 Compute the slope of the line tangent to the level curve at P, and verify that the tangent line is orthogonal to the gradient at that point. X Find the derivative of f(x,y) = 1 - 16 64 dy 4x dx What is the slope of the tangent line to the level curve at P -51-V5 ? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. 21/5 A. The slope is 5 O B. The slope is undefined, so the tangent line is vertical. Verify that the tangent line is orthogonal to the gradient at P|-7, - 15 . Select the correct choice below and fill in the answer boxes to complete your choice. O A. 58 1290 The slope of the tangent line, m, can be used to write a vector in the direction of the tangent line, (1,m) . The dot product of this vector and the gradient 290 580 is 0, so they are orthogonal. B. The tangent line slope is undefined, so it is a vertical line. The gradient (, ) is horizontal, so it is orthogonal to the tangent line.Find the directions in the xy-plane in which the function f(x,y) =7 -4x - 3y" has zero change at the point P(2,2, - 21). Express the directions in terms of unit vectors. What is the unit vector in a direction of zero change with a positive x-component? 31/11 41/11 11 11 (Type exact answers, using radicals as needed.)Consider the function f(x,y,z) = 3x" + 2y