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Does the function satisfy the hypotheses of the mean value theorem on the given interval? f(x) = 4x^2 + 3x + 4, [β1, 1] no, f is continuous on [β1, 1] but not differentiable on (β1, 1). no, f is not continuous on [β1, 1]. yes, f is continuous on [β1, 1] and differentiable on (β1, 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.
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