Question

I need someone to check my work and I need some help with number 2 selecting the statements that are true.

You may work with your classmates on this take home test. Have fun and answer all of the questions correctly. Please show all work, except for problems like multiple choice or matching. 1) Suppose a plane has x, y, and z-intercepts of 4, 3, and -12 respectively a) Find the derivative in the y-direction. b) Find Duof(x.y) Y-iretiun +3 7A ) What is the direction (as a two-dimensional vector) of steepest slope for this plane? / SteEpest slepe is at paint d) What is the steepest slope (as a scalar) for this plane? Heapesf slof al ung the tineotxardy inteap tnat is shortest dist400 こダ y t3 4-5ag yhypatinu tist メニッp ン 3 メ ン43 2) Select any true statements about the two-dimensional gradient V steepest slope l12)12/5 S a) If Vf Lû, the slope of the tangent plané in the direction of û is zero. b) Assuming û = (u4,.u,), Dif(x, y)= f,(x, y) - u, +f, (x, y) -u, c) -Vf gives the maximum slope of the tangent plane. d) If f Vf, the slope of the tangent plane is greatest in the y-direction. e) If Vf and û point in opposite directions, Df(x, y) = -Vf f) If Vf Ln, then Daf(x, y) 0.

Answer 1

c) gradient of f(x, y) in required direction lie, pf = fait fyJ -zi+(-3) 5 DIfl 3 1210-25| > Vest (3) >+4 slot → Slo 2) I think it's option é accoxding to the defination of the two-dimensional gradient.