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1) For each of the following state whether it is true or false. If true give...

1) For each of the following state whether it is true or false. If true give one sentence exolanation. If false, give counterexample.

a)If f is differentiable on (0,1) and f is increasing on (0,1) then f' > 0 on (0,1)

b)Suppose that f is thrice differentiable function defined on (-1,1). Suppose that the second order Taylor polynomial of f at 0 is 1-x^2. Then f has a local extremum at 0.
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