Multivariate Calculus

16 a-e

16. Consider the function f defined by f(x, y) = 8 - al - 3y?. a. Determine f(x, y) and fy(x, y). b. Find parametric equations in R for the tangent line to the trace f(x, 1) at = 2 c. Find parametric equations in R* for the tangent line to the trace f(2, y) at 7 = 1. d. State respective direction vectors for the two lines determined in (b) and (C). e. Determine the equation of the plane that passes through the point (2, 1, f(2, 1)) whose normal vector is orthogonal to the direction vectors of the two lines found in (b) and (c). f. Use a graphing utility to plot both the surface = = 8 - 23 - 3y' and the plane from (e) near the point (2, 1). What is the relationship between the surface and the plane