Triangle D E F is shown with point P at the center. Lines are drawn from each point of the triangle to point P. Line segments are drawn from point P to the sides of the triangle to form right angles and line segments P H, P J, and P G. The length of F J is 3 x minus 1, the length of J E is x + 3, the length of H E is 4 y minus 3, and the length of H D is 9. Given that point P is equidistant from the vertices of ΔDEF, what is EF?

EF =

nah jk

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.