Tyler finds an expression v(x) for that gives the volume of a open-top box in cubic inches in terms of the length x in inches of the cutout squares used to make it.

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.

Determine the solution for mc001-1.jpeg

Find all critical values for the function f(r)=2r(6r^2+8) and then list them (separated by commas) in the box below.