A function f and a point P are given. Let 0 correspond to the direction of the directional derivative. Complete parts a. through e. + 2y²), P ( 3.- √5) f(x,y)= In (1+6x² +2 (Type your answer alans. Type all exact answer is a comma separate answers as itu.) What angles are associated with the direction of zero change? C (Type your answer in radians. Type an exact answer in terms of . Use a comma to separate answers as needed.) c. Write the directional derivative at P as a function of 0; call this function g(0). g(0) = (Simplify your answer. Type an exact answer, using radicals as needed.) d. Find the value of 0 between 0 and 2x that maximizes g(0) and find the maximum value. What value of 0 maximizes g(0)? 0= (Type your answer in radians. Type an exact answer in terms of .) What is the maximum value? g(0) = (Type an exact answer, using radicals as needed.) e. Verify that the value of 0 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? O No Yes
A function f and a point P are given. Let 0 correspond to the direction of the directional derivative. Complete parts a. through e. + 2y²), P ( 3.- √5) f(x,y)= In (1+6x² +2 (Type your answer alans. Type all exact answer is a comma separate answers as itu.) What angles are associated with the direction of zero change? C (Type your answer in radians. Type an exact answer in terms of . Use a comma to separate answers as needed.) c. Write the directional derivative at P as a function of 0; call this function g(0). g(0) = (Simplify your answer. Type an exact answer, using radicals as needed.) d. Find the value of 0 between 0 and 2x that maximizes g(0) and find the maximum value. What value of 0 maximizes g(0)? 0= (Type your answer in radians. Type an exact answer in terms of .) What is the maximum value? g(0) = (Type an exact answer, using radicals as needed.) e. Verify that the value of 0 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? O No Yes
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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