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QUESTION 3 Let f be a function of x and y, and suppose that f(1,0) = 5. Suppose that v/(1,0) = (-3,4) Consider the following statements about vf(1,0). O|V/(1,0)| is the size of the biggest directional derivative of f at the point (1,0)- (i) The vector V/(1,0) is orthogonal to the curve f(x.y) =5 (H) At (1,0), f changes most rapidly in the direction of the unit vector (1,0) Which of the above statements is correct? O a. (i) and (ii) are correct. Ob.(1) and (ii) are correct. O.() and (i) are correct. Od. (). (i), and (i) are all correct.

QUESTION 3 Let f be a function of x and y, and suppose that f(1,0) = 5. Suppose that v/(1,0) = (-3,4) Consider the following statements about vf(1,0). O|V/(1,0)| is the size of the biggest directional derivative of f at the point (1,0)- (i) The vector V/(1,0) is orthogonal to the curve f(x.y) =5 (H) At (1,0), f changes most rapidly in the direction of the unit vector (1,0) Which of the above statements is correct? O a. (i) and (ii) are correct. Ob.(1) and (ii) are correct. O.() and (i) are correct. Od. (). (i), and (i) are all correct.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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QUESTION 3 Let f be a function of x and y, and suppose that f(1,0) =5. Suppose that vf(1,0) = (-3,4> Consider the following statements about Vf(1,0)- (1) |Vf(1,0)) is the size of the biggest directional derivative of f at the point (1.0). (i) The vector Vf(1,0) is orthogonal to the curve f(x,v) = 5 (ii) At (1,0), f changes most rapidly in the direction of the unit vector (1.0) Which of the above statements is correct? O a. (i) and (i) are correct. O b.() and (i) are correct. O. () and (i) are correct. O d.(1). (ii), and (i) are all correct.
Transcribed Image Text:QUESTION 3 Let f be a function of x and y, and suppose that f(1,0) =5. Suppose that vf(1,0) = (-3,4> Consider the following statements about Vf(1,0)- (1) |Vf(1,0)) is the size of the biggest directional derivative of f at the point (1.0). (i) The vector Vf(1,0) is orthogonal to the curve f(x,v) = 5 (ii) At (1,0), f changes most rapidly in the direction of the unit vector (1.0) Which of the above statements is correct? O a. (i) and (i) are correct. O b.() and (i) are correct. O. () and (i) are correct. O d.(1). (ii), and (i) are all correct.
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