# Applying the First(a) find the critical nintervals on which th(c) apply the First7. g(x) = 2x + 5 cos x, 0, 278. f(x) = sin 2x, [0, 27]Using Rolle's Theorem In Exercises 9-12, determinewhether Rolle's Theorem can be applied to f on the closedinterval a, b. If Rolle's Theorem can be applied, find allvalues of c in the open interval (a, b) such that f'(c) = 0. IfRolle's Theorem cannot be applied, explain why not.and (d) use aextrema,бх +27. f(x) = x2 -6x8t29. f()49. f(x) = x3 - 3x - 6, [-1, 2]x+410. f(x) = (x- 2) (x + 3)2, [-3, 2]31. f(x) =[-2, 2]11. f(x)sin1 - x2'33. f(x) = coSsin12. f(x) = sin 2x, [-T, T]3TX34. f(x)22Using the Mean Value Theorem In Exercises 13-18,determine whether the Mean Value Theorem can be applied tof on the closed interval a, b. If the Mean Value Theorem canbe applied, find all values of c in theMotion Along a Lins(t) describes the motivelocity function of ththe time interval (s) ondirection. (c) Identifyis moving in a negatiwhich the particle chaopen interval (a, b) such thatf (b) - f(a)b- af'(c) =If the Mean Value Theorem canpot be applied, explain why not.13. f(x) x2/3, [1, 835. sid = 3t -2121[1, 4]14. f(x)Finding Points of Ipoints of inflection a15. f(x) = 15 - x| [2,6]3x. [-1, 1]the function.16. f(x) = 2x37. f(x) = x 9x238. f(x) = 6x4 -39. g(x) = x x +540. f(x) 3x -5x341. f(x)17. f(x) = x- cos x,2' 2x218. f(x) = x 2x, [0,4]19. Mean Value TheoremЗх —Can the Mean Value Theorem beapplied to the function=XtcoSx,1f(x) =42. f(x) ==tan(0,4on the interval [-2, 1]? Explain.Using the Secondfind all relative extr20. Using the Mean Value Theorem(a) For the function f(x) Ax Bx + C, determine thevalue of c guaranteed by the Mean Value Theorem on theinterval [xj, x2](b) Demonstrate the result of part (a) for f(x) = 2x2 - 3x +1on the interval 0, 4]Derivative Test where43. f(x) = (x +9)244. f(x) = x4 - 2x245. g(x) = 2x2(1- x246. h(t) = t - 4 t+11

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