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  3. let f: [0 1] ? r be a function of the class c ^ 2.

Let f: [0 1] ? R be a function of the class c ^ 2...

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Advance Math

Let f: [0 1] ? R be a function of the class c ^ 2 thatsatisfies the differential equation f '' (x) = e^xf(x) for all x in(0,1). Show that if x0 is in (0,1) then f can not have a positivelocal maximum at x0 and can not have a negative local minimum atx0. If f (0) = f (1) = 0, prove that f = 0

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