Consider the function F(x, y, z) = x2 â yz + x2 and the point P(-3,5, -1). a. Find the direction (this doesn't need to be a unit vector) in which F increases most rapidly at the point P.
b. Compute the maximum rate of change for F at P.
c. The level surface of F which passes through P is S: x^2 â yz + x^2 = 15. Find an equation in standard form for the tangent plane to s at P.
d. Find a set of parametric equations for the line normal to s at P.