11. [5] Consider the cubic function (x) = x + bx + cx + d. Show...

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11. [5] Consider the cubic function (x) = x + bx + cx + d. Show that the sum of the critical numbers is - 20. Part D: Communication [10 marks] 12. a) [4'] Given the differentiable function that f (2) = 1 and f (4) = 10. Is that possible to have a local extrema in the interval of [2, 4]? Is that able to particularly tell the extrema is maximum or minimum? b) [4'] How about non-differentiable function? Is that possible to have an extrema? Draw diagram to supporting your answer. 11. [5] Consider the cubic function (x) = x + bx + cx + d. Show that the sum of the critical numbers is - 20. Part D: Communication [10 marks] 12. a) [4'] Given the differentiable function that f (2) = 1 and f (4) = 10. Is that possible to have a local extrema in the interval of [2, 4]? Is that able to particularly tell the extrema is maximum or minimum? b) [4'] How about non-differentiable function? Is that possible to have an extrema? Draw diagram to supporting your answer.