# Need Help. It's urgent

• 5. Given the function F(x,y,z,t)=xcos(t)+ysin(t)+z(t^2+t-2). Find the points, if any,
on the curve r(t)=<cos(t), sin(t), t> where this function assumes extreme values.

7. The temperature at a point P(x,y,z) is given by T=200e^(-x^2-3y^2-9z^2), where T is measured in celsius and x, y, z are in meters.

a) Find the rate of change in the temperature at the point P(2,-1,2) in the direction toward the point Q(3,-3,3)
b) In what direction does the temperature increase fastest at P?
c) Find the maximum rate of increase at P.
d) In what direction(s) does the temperature has no change at P?

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• The temperature at a point P(x,y,z) is given by T=200e^(-x^2-3y^2-9z^2), where T is measured in celsius and x, y, z are in meters.

a) Find the rate of change in the temperature at the point P(2,-1,2) in the direction toward the point Q(3,-3,3)
rate of change = (T(Q)-T(P))/distance from P to Q

b) In what direction does the temperature increase fastest at P?
Partial derivative dT/dx, dT/dy, dT/dz ... @P

c) Find the maximum rate of increase at P.
examine limits at P

d) In what direction(s) does the temperature has no change at P?
no change = rate of change = 0