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Let f: [a, b] -> R be a function, conti...

Let `f: [a, b] -> R` be a function, continuous on `[a, b]` and twice differentiable on `(a, b)`. If, `f(a) = f(b) and f'(a) = f'(b)`, then consider the equation `f''(x) - lambda (f'(x))^2 = 0`. For any real `lambda` the equation hasatleast M roots where `3M + 1` is

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