Question: (a) Show that it is tmpossible to have a polynomial function, p(x), which satisfies all three of the following conditions: (1) p(1) =3 (%) y

(a) Show that it is tmpossible to have a polynomial function, p(x), which satisfies all three of the following conditions: (1) p(1) =3 (%) y = p(z) passes through the origin (i) p(z) strictly decreasing over its domain 1 (b) Suppose that f(z) is a continuous function and that / f(z)dz = % Show that there is at least one point c 0 in (0,1) so that f(c) = c2

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