Suppose that the function f is continuous at [1,4] derivable at (1, 4) and still holds f (1) = 3 and f (4) = 12. Prove that: a) the function g satisfies the conditions of the Rolle theorem in space [1, 4].
b) there is at least one such that the tangent to the graph of f at point A (ξ, f (ξ)) passes through the origin of the axes.