shl x stude X Conte X Conte X Bb 24034 X Bb 23646 X f (3) Fa X New 1 X heast-2-prod-fleet01-xythos.content.blackboardcdn.com/5ddb108fe0c42/24034673?X-Blackboard-$3-Bucket=learn-ap... 2 / 5| - 100% + Q1. Consider the function f (x, y, z) = 12 + z In(x2 + y?) - 223 in R' defined for all (x, y, z) with x2 + y? > 0. (a) Find an equation for the tangent plane to the level surface S : f (1, y, z) =0 in R' at the point Q = (1, 0, 1) E S and a normal vector to S at Q. [4 marks] (b) Find the direction in which the function f(r, y, 2) increases most rapidly at the point Q - (1,0, 1). What is the maximal rate of increase of f at Q? [2 marks]