T(rauses volumetric heating to vary according to

q̇(x) = q̇₀[1 - (x/L)]

where q̇₀ has a constant value of 180 kW/m³ and the slab thickness, L, is 0.06 m. The thermal conductivity of the slab material is 0.6 W/m · K. The boundary at x = L is perfectly insulated, while the surface at x = 0 is maintained at a constant temperature of 320 K. 

a. Determine an expression for T(x) in terms of X, L, k, q̇₀, and T₀.
b. Where in the slab will the maximum temperature occur?
c. What is the value of T_max?