P(x) x (2x+1)3 et P be a quadratic polynomial such that P(0) = -1 and dx is a rational function i.e., a quotient of two polynomials). Find the value of the derivative P'(0). Justify your answer. Hints: Write P(x) = ax + bx + c. Then P(0) and P'(0) can be expressed in terms of the coefficients a, b and c of P. What are they? Decompose P(x)/(x (2x + 1)) into partial fractions (with some unknown constants for the nu- merators) and see what is the general form of an antiderivative of each of them. These antiderivatives are supposed to sum up to a rational function themselves, which means that no logarithmic terms are allowed. This implies that two of the five unknown constants in the partial fraction decomposition must be zero. Finally, convert the above partial fraction decomposition into a polynomial equation and compare the coefficients at the corresponding powers of x on both sides to find the answer.]