If the following pattern is valid, construct a formal proof in fitch. if it is invalid, give a counterexample using tarski’s world. to give a counterexample in these cases, you will have to come up with sentences of the blocks language that fit the pattern, and a world that makes those specific premises true and the conclusion false. submit both the world and the sentence file. in the sentence file, list the premises first and the conclusion last.

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.