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15.5.37 Question Help A function f and a point P are given. Let θ correspond to the direction of the directional derivative. Complete parts (a) through (e) #x,y)-10-4x2-3y2, P(3,4) a. Find the gradient and evaluate it at P The gradient at P is b Find the angles θ with respect to the positive x-axis associated with the directions of maximum increase, maximum decrease, and zero change What angle(s) is/are associated with the direction of maximum increase? (Type any angles in radians between 0 and 2π. Type an exact answer, using π as needed. Use a comma to separate answers as needed) What angle(s) is/are associated with the direction of maximum decrease? (Type any angles n radians between 0 and 2π. Type an exact answer, using π as needed. Use a comma to separate answers as needed What angle(s) is/are associated with the direction of zero change? The angle(s) associated with the directions of zero change is/are Type any angles in radians between 0 and 2T. Type an exact answer, using a as needed. Use a comma to separate answers as needed.) c. Write the directional derivative at P as a function of 6, call this function g() g(e) d. Find the value of θ that maximizes g(6) and find the maximum value, what value of θ maximizes g(8)? (Type any angles in radians between 0 and 2π. Type an exact answer, using π as needed) What is the maximum value? Type an exact answer, using radicals as needed.)

Answer 1

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