The function f (x, t) = 1 2 t ex2/4t describes the temperature profile along a metal rod
Chapter 14, Problem 78(choose chapter or problem)
The function f (x, t) = 1 2 t ex2/4t describes the temperature profile along a metal rod at time t > 0 when a burst of heat is applied at the origin (see Example 11). A small bug sitting on the rod at distance x from the origin feels the temperature rise and fall as heat diffuses through the bar. Show that the bug feels the maximum temperature at time t = 1 2 x2.
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