P x et P be a quadratic polynomial such that P 0 1 and x 2x

Last updated: 2/10/2023

P x et P be a quadratic polynomial such that P 0 1 and x 2x 1 i e a quotient of two polynomials Find the value of the derivative P 0 Justify your answer Hints da is a rational function 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 x on both sides to find the answer