Question: The function describes the temperature profile along a metal rod at time t > 0 when a burst of heat is applied at the origin

The function f(x, t) = 1 2nt -x/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.

EXAMPLE 11 The Heat Equation Show that u(x, 1) = t> 0, satisfies the heat equation at = au x 1 2nt e-(x/4t),

f(x, t) = 1 2nt -x/4t

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