18. [-/0.33 Points] DETAILS SCALCET8 4.1.057. MY NOTES ASK YOUR TEACHER Find the absolute maximum and absolute minimum values of f on the given interval. f(t) = 2 cos(t) + sin(2t), [0, 7/2] absolute minimum value absolute maximum value 19. [-/0.33 Points] DETAILS SCALCET8 4.1.058. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the absolute maximum and absolute minimum values of f on the given interval. f(t) = 8t + 8 cot(t/2), [7/4, 7Tt/4] absolute minimum value absolute maximum value 20. [-/0.33 Points] DETAILS SCALCET8 4.1.068. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Use calculus to find the absolute maximum and minimum values of the function. f(x) = 6x - 12 cos(x), -2 S XSO (a) Use a graph to find the absolute maximum and minimum values of the function to two decimal places. maximum minimum (b) Use calculus to find the exact maximum and minimum values. maximum minimum21. [-/0.33 Points] DETAILS SCALCET8 4.2.005. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. (Enter your answers as a comma-separated list.) f(x) = 3x2 - 6x + 4, [-1, 3] C= Need Help? Watch It 22. [-/0.33 Points] DETAILS SCALCET8 4.2.007. MY NOTES ASK YOUR TEACHER Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. (Enter your answers as a comma-separated list.) f(x) = sin =),28. [O.16/0.33 Points] PREVIOUS ANSWERS SCALCETB 4.2.510.XP. Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? ASK YOUR TEACHER PRACTICE ANOTHER W) = Xj4, [1,8] O Yes, it does not matter if fis continuous or differentiable; every function satisfies the Mean Value Theorem. 0 Yes. fis continuous on [1, S] and differentiable on (1, 8). O No, fis not continuous on [1, 8]. O No, fis continuous on [1, 8] but not differentiable on (1, B). Q There is not enough information to verify if this function satisfies the Mean Value Theorem. W If it satisfies the hypotheses, find all numbers 5 that satisfy the conclusion of the Mean Value Theorem. (Enter your answers as a comma-separated list. If it does not satisfy the hypotheses, enter DNE). c= mm x 23. [0.16/O.33 Points] PREVIOUS ANSWERS SCALCET8 4.2.011. Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? ASK YOUR TEACHER PRACTICE ANOTHER f(x) = 5x2 2x + 3, [0,2] O Yes, it does not matter if fis continuous or differentiable, every function satifies the Mean Value Theorem. 0 Yes, fis continuous on [0, 2] and differentiable on (O, 2) since polynomials are continuous and differentiable on R. O No, fis not continuous on [0, 2]. O No, fis continuous on [0, 2] but not differentiable on (0, 2). Q There is not enough information to verify if this function satifies the Mean Value Theorem. v7 If it satisfies the hypotheses, find all numbers c that satisfy the conclusion of the Mean Value Theorem. (Enter your answers as a comma-separated list. If it does not satisify the ypotheses, enter DNE). C: Need Help? 24. [0.171033 Points] PREVIOUS ANSWERS SCALCET8 4.2.017. ASK YOUR TEACHER PRACTICE ANOTHER Let f(x) = (x 7 3)'2. Find all values ofc in (1, 4) such that f(4) 7 f(1) = f'(c)(4 7 1). (Enter your answers as a comma7separated list. If an answer does not exist, enter DNE.) C= Based off of this information, what conclusions can be made about the Mean Value Theorem? J14) - f(1) O This contradicts the Mean Value Theorem since fsatisfies the hypotheses on the given interval but there does not eXist any c on (1, 4) such that f'(c) : 4 1 O This does not contradict the Mean Value Theorem since fis not continuous at x : 3. f(4) -f(1)_ O This does not contradict the Mean Value Theorem since fls continuous on (1, 4), and there exists a c on (1, 4) such that f'(c) = 4 1 O This contradicts the Mean Value Theorem since there exists a c on (1, 4) such that f'(c) : O Nothing can be concluded. 25. [-/0.33 Points] DETAILS SCALCETB 4.2.025. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER If f(4) = 7 and f '(X) 2 3 for 4 S x S 8, how small can f(8) possibly be? :1 Need Help? 26. [-/0.33 Points] DETAILS SCALCET8 4.2.026. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Suppose that 2 s f '(x) S 5 for all values of X. What are the minimum and maximum possible values of RS) f(4)? 27. [-/0.33 Points] DETAILS SCALCETB 4.2.501 .XP. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers 5 that satisfy the conclusion of Rolle's Theorem. (Enter your answers as a comma-separated list.) f(x) : 4 24x + 3x2, [3, 5] Need Help