Compute the directional derivative of T(x,y,z)=200e^(-x^2-3y^2-9z^2) at the point (2,-1,2) in the direction toward the point...

Compute the directional derivative of T(x,y,z)=200e^(-x^2-3y^2-9z^2) at the point (2,-1,2) in the direction toward the point (3,-3,3). What is the maximum rate of change of T at the point (2,-1,2)?

I have solve this by mathematica...

Expert Solution

milcah answered 2 years ago

Calculate the directional derivative of f(x,y,z)=x(y^2)+y((1-z)^(1/2)) at the point P(1,−2,0) in the direction of the vector...

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A) Find the directional derivative of the function at the given point in the direction of...

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The temperature at a point (x,y,z) is given by T(x,y,z)=200e^(-x^2-y^2/4-z^2/9) , where T is measured in...

The temperature at a point (x,y,z) is given by T(x,y,z)=200e^(-x^2-y^2/4-z^2/9) , where T is measured in degrees Celsius and x,y, and z in meters. just try to keep track of what needs to be a unit vector. a) Find the rate of change of the temperature at the point (1, 1, -1) in the direction toward the point (-5, -4, -3). b) In which direction (unit vector) does the temperature increase the fastest at (1, 1, -1)? c) What is...

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