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2) a] f(x)={ 1/2 -x ; x<1/2 , [1/2 -x]^2 ; x>=1/2
For MVT to be applied, the function should be differentiable in (0,1)
3) a)
f(1) = 0
f '(1) > 0
= > f'(x) >0 for all x >1
So f(x) is increasing in all x belongs x>1
Therefore f(x) > 0 for all x belongs to ( 1, inf.)
4) b)
If the tangent to a curve is parallel to x axis , then f'(x) =0
Here it is true for x = 2
For x=2, y = -1
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Moderation Team
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