A function f and a point P are given. Let correspond to the direction of the directional derivative. Complete parts a. through e.1f(x,y)= In (1+6x²+6y²), P-√6)4a. Find the gradient and evaluate it at P.2421180 5211b. Find the angles (with respect to the positive x-axis) between 0 and 2x associated with the directions of maximum increase, maximum decrease, and zero change. What angles are associated with the direction of maximum increase?- (-10,5)-+273(Type your answer in radians. Type an exact answer in terms of Use a comma to separate answers as needed.)What angles are associated with the direction of maximum decrease?The gradient at Pistantan10,53+ T(Type your answer in radians. Type an exact answer in terms of Use a comma to separate answers as needed.)What angles are associated with the direction of zero change?- 10/5)+.tan - (-10,5)+3701tan332(Type your answer in radians. Type an exact answer in terms ofc. Write the directional derivative at P as a function of ; call this function g(*).2480 √5g(0) 211 cos- 211 sinė(Simplify your answer. Type an exact answer, using radicals as needed.)d. Find the value of between 0 and 2x that maximizes g(0) and find the maximum value. What value of maximizes g(+)?e= tan3+2TT.(Type your answer in radians. Type an exact answer in terms of )What is the maximum value?Use a comma to separate answers as needed.)10√5YesO No(...)8/509g(*)=211(Type an exact answer, using radicals as needed.)e. Verify that the value of that maximizes g corresponds to the direction of the gradient. Verify that the maximum value of g equals the magnitude of the gradient. Are the values from part d consistent with the values from parts a and b?

Given the function fx,y=ln1+6x2+5y2 and point P as P14,-5. # As per the guidelines we are entitled…

A function f and a point P are given. Let correspond to the direction of the directional derivative. Complete parts a f(x,y)= In (1+6x²+5y²), P.- √5] a. Find the gradient and evaluate it at P. 24 80-5 211 211 b. Find the angles + (with respect to the positive x-axis) between 0 and 2x associated with the directions of maximum 10./5 The gradient at P is tan + 2x (Type your answer in radians. Type an exact answer in terms of Use a comma to separate answers as needed.) What angles are associated with the direction of maximum decrease? 10,5 tan +T

A function f and a point P are given. Let correspond to the direction of the directional derivative. Complete parts a f(x,y)= In (1+6x²+5y²), P.- √5] a. Find the gradient and evaluate it at P. 24 80-5 211 211 b. Find the angles + (with respect to the positive x-axis) between 0 and 2x associated with the directions of maximum 10./5 The gradient at P is tan + 2x (Type your answer in radians. Type an exact answer in terms of Use a comma to separate answers as needed.) What angles are associated with the direction of maximum decrease? 10,5 tan +T

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 94E

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