Please Help with Multivariable Calculus Gradient Vector Questions Note Q9 Part a) is current, Can't figure out part b. Any help is greatly appreciated, Thank you!

Assignment06: Problem 7 (1 point) If the gradient of f is Vf : 3:13}: + z} yziand the point P : (4, 8, 8) lies on the level surface f(:t:, y,2:) : 0, nd an equation for the tangent plane to the surface at the point P. z: Assignment06: Problem 9 (1 point) Consider the function x, y) = (e2 52:) sin(y). Suppose S is the surface 2 = f(1t', y). in] Find a vector which is perpendicular to the level curve of fthrough the point (5, 3) in the direction in which fdecreases most rapidly. vector = -(sin(3)(e"5 - 5)i + (e"5 - 25)cos(3)j) [b] Suppose 1"; : 1; + 23 + a; is a vector in 3-space which is tangent to the surface S at the point P lying on the surface above (5, 3). What is a? a: as Assignment06: Problem 17 (1 point) The temperature at a point (x.y,z) is given by T(:t:, y, z) = 2006523'2/4z2/9, where T is measured in degrees Celsius and x,y, and z in meters. There are lots of places to make silly errors in this problem; just try to keep track of what needs to be a unit vector. Find the rate of change of the temperature at the point (-1, -1, 1) in the direction toward the point (-1, 4, 5). In which direction (unit vector) does the temperature increase the fastest at (-1, -1, 1)? ( =:, E:, =:) What is the maximum rate of increase of T at (-1, -1, 1)