Explain please #13 and #26

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7. f(x) - sin(x/2), [T/2, 3T/ 2] 8. /f (x) = x+1/x, [2, 2] 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 not contradict Rolle's Theorem? 10. Let f(x) = tan x. Show that f(0) = f(7) but there is no number c in (0, 17) such that f' (c) = 0. Why does this not contradict Rolle's Theorem? 11-14 Verify that the function satisfies the hypotheses of the Mean Value Theorem on the given interval. Then find all num- bers c that satisfy the conclusion of the Mean Value Theorem. 11. f(x) = 2x2 - 3x + 1, [0, 2] 12. f (x) = x3 - 3x + 2, [-2, 2] 13. f(x) = Vx. [0, 1] 14. f(x) - 1/x, [1. 3] 15-16 Find the number c that satisfies the conclusion of the Mean Value Theorem on the given interval. Graph the fune the secant line through the endpoints, and the tangent line23. (a) Show that a polynomial uous on [0, 8] real roots. not satisfy the (b) Show that a polynomial of degree n has at most n real roots. theses of 24. (a) Suppose that f is differentiable on IN and has two roots umbers c Show that f' has at least one root. (b) Suppose f is twice differentiable on R and has three roots. Show that f" has at least one real root. (c) Can you generalize parts (a) and (b)? 25. If f(1) = 10 and f'(x) > 2 for 1