3-Dimensional Calculus problem?
I'm stuck on this homework problem 
Let T(x,y,z) = 100 +x^2+y^2 represent the temperature at each point on the sphere x^2+y^2+z^2=50. Find the max temperature on the curve formed by the intersection of the sphere and the plane x-z=0.
Thanks for any help you can provide.
Comments
Find where the sphere and plane intersect.
x² + y² + x² = 50
2x² + y² = 50
Use method of Lagrange multipliers to maximize f(x, y) = 100 + x² + y²
subject to the constraint g(x, y) = 2x² + y² - 50.
∂f/∂x = λ(∂g/∂x)
2x = λ(4x) [1]
∂f/∂y = λ(∂g/∂y)
2y = λ(2y) [2]
[2] / [1] and x ≠ 0:
y/x = y/(2x)
y = 0
2x² = 50
x = ±5
f(±5, 0) = 100 + (±5)² + 0²
f(±5, 0) = 125
[1] / [2] and y ≠ 0:
x/y = 2x/y
x = 0
y² = 50
y = ±5sqrt(2)
f(0, ±5sqrt(2)) = 100 + 0² + 50
f(0, ±5sqrt(2)) = 150 <--- max temperature