1. The problem statement, all variables and given/known data A cannonball is heated with with temperature distribution T(x,y,z)=60(y2+z2-x2). The cannonball is a sphere of 1 ft with it's center at the origin a) Where are the max and min temperatures in the cannonball, and where do they occur? 2. Relevant equations [itex]\nabla[/itex]f=λ[itex]\nabla[/itex]g Where g is the the constraint and λ is the common ratio. [itex]\nabla[/itex]= fx i + fy j + fz k 3. The attempt at a solution The cannonball is the restraint so λ[itex]\nabla[/itex]f = 2xλ i + 2yλ j + 2zλ k [itex]\nabla[/itex]T = -120x i + 120y j + 120z k 2xλ = -120x, λ= -60 2yλ = 120y, λ = 60 2zλ = 120z, λ = 60 I don't know where to go from here. All the variables canceled so I can't relate them to each other, and the λs are different.