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Given a continuous function f on [0, 1]. Suppose f'(0) and f''(0) both exits on (0,...

Given a continuous function f on [0, 1]. Suppose f'(0) and f''(0) both exits on (0, 1). Determine whether the following general statements about f are true or not. If not, give a counter-example

1. Suppose f(1/2) is a local extreme value of f, then f'(1/2) = 0?

2. Suppose f '( 1 2 ) = 0, then f(1/2) is a local extreme value of f.

Math   Calculus   
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