explain please #7 and 8

220 4. D a function that is continuous on [O, 8] 23. (a) where f(0) = 1 and f(8) = 4 and that does not satisfy the conclusion of the Mean Value Theorem on [0, 8]. (b 5-8 Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c 24. that satisfy the conclusion of Rolle's Theorem. 5. f (x) = 2x2 - 4x + 5, [-1, 3] 6. f (x) = x3 - 2x2 - 4x + 2, [-2, 2] 7. f(x) = sin(x/2), [1/2, 37/2] 25. 8. f(x) = x+ 1/x, [z, 2] 26 9. Let f(x) = 1 - x2/3. Show that f(-1) = f(1) but there is no number c in (-1, 1) such that f'(c) = 0. Why does this 27 not contradict Rolle's Theorem? 10. Let f(x) = tan x. Show that f(0) = f( TT) but there is no number ~ in (Q such that file) - 0 Why does this