Given the function g(x) = x^2 +5x+14, determine the average rate of change over the the interval 1

Factor a^3 - 3 + 3a^2 - a. a) (a - 1)(a + 1)(a + 3) b) (a^2 + 1)(a - 3) c) (a^2 - 3)(a + 1)

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.

What are the values of each variable in the diagram below?