Suppose f: [0,2]-> R is differentiable. f(0)=0, f(1)=2 and f(2)=2. Prove that

1. There is such that f'( ) =0

2. There is such that f'(c_2)=2 and

3. There is such that f'( =1/2

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- Apr 24th 2010, 07:16 PMalice8675309prove there is a c_1
Suppose f: [0,2]-> R is differentiable. f(0)=0, f(1)=2 and f(2)=2. Prove that

1. There is such that f'( ) =0

2. There is such that f'(c_2)=2 and

3. There is such that f'( =1/2 - Apr 24th 2010, 07:48 PMmaddas
For (1) and (2), use the mean value theorem on the intervals [1,2] and [0,1] respectively. Since a derivative always has the intermediate value property (Darboux's theorem), it follows that there is a between and where the derivative is 1/2.

- Apr 24th 2010, 07:55 PMalice8675309