Let f be continuous on [a, b] and assume...

Let f be continuous on [a, b] and assume the second derivative f" exists on (a, b). Suppose that the graph of f and the line segment joining the point `(a,f(a)) and (b,f(b))` intersect at a point `(x_0,f(x_0))` where `a < x_0 < b.` Show that there exists a point `c in(a,b)` such that `f"(c)=0.`

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