Question

The temperature at the point (x,y,z) in space is given by T(x,y,z)=x+yz. A fly is at the point (1,2,1). In what Direction should he begin to fly to cool off as quickly as possible?

Answer 1

the gradient vector is the vector that points in the greatest possible change in a function

Answer 2

so\[\nabla T(x,y,z)\]

Answer 3

What exactly is t? and the gradient vector deltaT is just 1i+2j right?

Answer 4

\[\nabla T=T_x\hat i+T_y\hat j+T_z\hat k\]

Answer 5

\(T_x\) is the partial derivative of T with respect to x. Take the partial derivative of T with respect to x; that will be the i-component of your vector
what do you get ?