CALCULUS:GRAPHICAL,NUMERICAL,..-PACKAGE
5th Edition
ISBN: 9780133320381
Author: Finney
Publisher: SAVVAS L
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Find the directional derivative of the function at P in the direction of V.
f(x,y) = x³-y³, P(5,4), v = √² (i+j)
a.
(922.5)√√2
b. (-5.252.5)√√2
D
C.
(1,845.0)√√2
d. (5,252.5)√2
e. (1,677.5)√√2
Find the directional derivative of f(x, y, z) = xy + z³ at the point P = (3, −4, −3) in the direction pointing to the origin.
(Give an exact answer. Use symbolic notation and fractions where needed.)
Dof(P) =
Consider the following function which is defined for all x and y:
f(x, y) = 2(1-p²)x²y² - x² - y² + 3pxy + 2x+4y+2
where p is a constant.
(a) Find the first order derivatives of f and enter them as functions of x, y and p
(b) Find the second order derivatives of f and enter them as functions of x, y and p
(c) For p = 1, find the stationary point (x*, y*).
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