Kara uses a hose to fill a swimming pool. The number of gallons of water in the pool, y, after x minutes can be modeled by the function shown. у 10 9 8 7 Gallons • (1, 4.4) 3 2 1 X Х 0 1 2 3 4 5 6 7 8 9 10 Minutes​

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.