Are the following statements True or False? Choose True if the statement is always True, and otherwise choose False.

? 1. The Closed Interval Method can be used to classify all local extrema of any function that is continuous on a closed interval. . 2. Even though the Second Derivative Test is not guaranteed to give a conclusion, it is sometimes far more efficient than doing the First Derivative Test. ? 3. It is possible to have a function f for which a) f'(x ) is continuous everywhere except x = 5, b) f' has a jump discontinuity at x = 5, AND c) f' (5) = 2. ? 4. The function f(x) = 5x-/ - x has a critical point at a = 0, but the Second Derivative Test cannot be used to classify this critical point because f'(0) / 0.? 7. For some functions, we can use either the First Derivative Test or the Second Derivative Test to classify the critical points, so we need to use our judgement to predict which will be more efficient. ? 8. The Intermediate Value Theorem is a huge part of why the First Derivative Test works. 9. The Closed Interval Method can be used to find the global extrema of the function g(x) = ~ ~ on the domain Dg = [0, 2021]. ? 10. The Closed Interval Method can be used to find the global extrema of the function g(x ) = on the domain D. = [-2021, 2021].? 5. The Second Derivative Test does not always produce useful information about critical points, even when we are able to compute the necessary derivatives. ? 6. The First and Second Derivative Tests are used to find critical values of a function. ? 7. For some functions, we can use either the First Derivative Test or the Second Derivative Test to