Put the given differential equation into form (3) in Section 6.3 (x − x0)2y'' + (x − x0)p(x)y' + q(x)y = 0 (3) for each regular singular point of the equation. Identify the functions p(x) and q(x). (x2 − 1)y'' + 3(x + 1)y' + (x2 − x)y = 0

Does the function satisfy the hypotheses of the mean value theorem on the given interval? f(x) = 4x^2 + 3x + 4, [−1, 1] no, f is continuous on [−1, 1] but not differentiable on (−1, 1). no, f is not continuous on [−1, 1]. yes, f is continuous on [−1, 1] and differentiable on (−1, 1) since polynomials are continuous and differentiable on . there is not enough information to verify if this function satisfies the mean value theorem. yes, it does not matter if f is continuous or differentiable; every function satisfies the mean value theorem.