Problem #PRU-111763

Problems Calculus Derivative Calculating a derivative Algebra and arithmetics Absolute value Inequalities containing absolute values Polynomials Quadratic polynomials Quadratic polynomial (other)
 15–16  4.0

Problem

The quadratic trinomials \(f (x)\) and \(g (x)\) are such that \(f' (x) g' (x) \geq | f (x) | + | g (x) |\) for all real \(x\). Prove that the product \(f (x) g (x)\) is equal to the square of some trinomial.