Energy -1.0 -0.5 0.5 1.0 20 The National Sleep Foundation advises that healthy adults need 8 hours of sleep per night. Try as we might this is difficult to do, and so we let a be the difference between the number of hours of sleep we actually got and the recommended 8 hours. Suppose the corresponding amount of energy you have, on a 0-100 scale, is given by the below function and above graph E(x) = 100 - 12x2 + x4 (a) According to this model, do we have more energy if we get 7 hours of sleep or 10 hours of sleep? Compute the exact values. (b) Compute the derivative E'(x). Assuming we are able to get between 7 and 10 hours of sleep, find the relevant critical points of E(x). (c) Assuming we are able to get between 7 and 10 hours of sleep, what amount of sleep minimizes our energy the following day