- #1
allenh98
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Homework Statement
The equation z(e^(xy)) + z^5 + y = 4 implicitly defines z as a function z = f(x,y) near (0,2,1)
(a) find df/dx and df/duy where x = 0, y = 0, and z = 1
(b) find the maximum rate of change of f at the point (0,2)
Homework Equations
sorry, my first post here not sure what i need to write in this section
The Attempt at a Solution
sol'n (a):
df/dx = yz(e^(xy))
df/dy = xz(e^(xy)) + 1
then i sub in the co-ords given to find
df/dx = 2
df/dy = 1
part (b) is where I am confused, since they only give us f at point (0,2), is it implied that we plug in f(0,2) and get z = 1 and solve the gradient?
here is what i did:
grad(f) = [yze^(xy)]i + [xe^(xy) + 1]j + [e^(xy) + 5z^4]k
substitute (0,2,1)
2i + j + 6k
= sqrt(41)