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Phantasy [73]
3 years ago
15

Find the maximum rate of change of f(x,y,z=x y/z at the point (2, -3, 5 and the direction in which it occurs. maximum rate of ch

ange:
Mathematics
1 answer:
kherson [118]3 years ago
6 0
f(x,y,z)=x+\dfrac yz
\implies \nabla f(x,y,z)=\left(1,\dfrac1z,-\dfrac y{z^2}\right)
\implies \nabla f(2,-3,5)=\left(1,\dfrac15,\dfrac3{25}\right)

The maximum rate of change is then

\|\nabla f(2,-3,5)\|=\dfrac{\sqrt{659}}{25}

which occurs in the direction of \nabla f(2,-3,5) above.
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