Find the maximum rate of change of f at the given point and the direction...

maduregimc

maduregimc

Answered

2021-12-22

Find the maximum rate of change of f at the given point and the direction in which it occurs.
f(x,y,z)=x2+y2+z2, (9,7,2)
maximum rate of change =
direction vector =

Answer & Explanation

Heather Fulton

Heather Fulton

Expert

2021-12-23Added 31 answers

f=xx2+y2+z2,yx2+y2+z2,zx2+y2+z2(9,7,2)
f=992+72+22,792+72+22,292+72+22=9,7,2134
Maximum rate of change =||f=92+72+22134=1
direction =f||f=9,7,2134
Jordan Mitchell

Jordan Mitchell

Expert

2021-12-24Added 31 answers

The formula is just him finding the derivative with respect to whatever slot the equation is in (f gradient = fx',fy',fz') and so forth.
karton

karton

Expert

2021-12-30Added 439 answers

where does that formula come from in?

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