Question

7. [-17 Points) DETAILS LARCALCET7 4.2.043.EP. Emal. Campbell, Outlook MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Consider the following function and closed interval FX)-3X, [1, 2] Is i continuous on the closed interval [1, 2]? Yes NO Iff is differentiable on the open interval (1, 2), find ). (If it is not differentiable on the open interval, enter ONE.) Find (1) and R2). (1) - R2) - Find for (a, b) - (1,21 b) - Determine whether the Mean Value Theorem can be applied to r on the closed interval (a, b). (Select all that apply) Yes, the Mean Value Theorem can be applied. No, because is not continuous on the closed interval (a, b). No, because is not differentiable in the open interval (a, b). None of the above. b) - ) if the Mean Value Theorem cannot be applied, explain why not. (Enter your of the Mean Value Theorem can be applied, find all values of c in the open interval (a, b) such that c) - answers as a comma-separated list. If the Mean Value Theorem cannot be applied, enter NA.) Need Help? Tuikte autor

Answer 1

3 on 7) Given f(c) = 350 [1,2] fü continuous on [1,2] since polynomial functions are all well-behaved. Also få diffesantiable everywhere especially on (1,2) and f'(x) = 3x327= 900.exists on (12) FCI) = 303-3 ; fca) = 3(2)3=24 Now f(b)-f(a) for [a, b]= [1, 2] is given by f(a) = f(1) b.-a fub) -fca) ba = 24 -3 2-1 al 2-1 [1,2] differentiable on (1,7) e. MUT Since fis continuous on there exists Ċ EC1,2) & F' C) = f(b)-f(), e. can be anplied cè. F'CC) - FC6) -fla) qc²= a1 =) c2 - b-a = 2) bra C2 = C= + among which C=V773 ~ 1-52 € (1,2) exists 3