Suppose we have that f(x) is twice different table at x 2 with f(2) = 1, f\'(2)

Question

Suppose we have that f(x) is twice different table at x 2 with f(2) = 1, f'(2) = 0. Determine which statement is true. (a) If f' changes in sign from negative to positive across x = 2 then f(x) has a local minimum at x = 2. (b) If f' changes in sign from positive to negative across x = 2 then f(x) has a local minimum at x = 2. (c) If f' is positive to the left and to the right of x = 2 then f(x) has a local minimum at x = 2. (d) If f' is negative to the left and to the right of x = 2 then f(x) has a local minimum at x = 2. (e) None of the above are true.

Explanation / Answer

Since we have f'(2) = 1 to f'(2) =0   There is no change in sign

it means there is no minima and maxima so we will go through ( e) option

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