Mathematics, 26.03.2021 22:30 ndkdidnfnk
Consider the function f(x, y) = -3x^2-2y^-2.
Find the directional derivative of f at the point (1,-4) in the direction given by the angle theta = 2pi/5.
Find the unit vector which describes the direction in which f is increasing most rapidly at (1,-4).
I have already confirmed the directional derivative to be exactly
-6cos(2pi/5) + 16sin(2pi/5)
I believed the unit vector should have been (cos(2pi/5), sin(2pi/5)), but when I checked my answer the only correct part was the sin(2pi/5). If the other part is not cos(2pi/5), then what is it and How would that be calculated or inferred?
A picture of the original format and my answers is also included.
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Consider the function f(x, y) = -3x^2-2y^-2.
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