Sketch the graph of a continuous function f(x) such that f(x) has roots at x=0 and x=2, but f'(x) has no roots for x in the interval [0,2]. Briefly explain why your sketch does not contradict Rolle's Theorem.
Just can't figure this one out...

Question

Sketch the graph of a continuous function f(x) such that f(x) has roots at x=0 and x=2, but f'(x) has no roots for x in the interval [0,2]. Briefly explain why your sketch does not contradict Rolle's Theorem. 
Just can't figure this one out...

allank · Answer

Have to go offline for a while, but whoever figures this one out, do post the solution :)

anonymous · Answer

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a possibility 
rolle's theorem also have one more condition that function should be diff at all points in chosen interval 
my function is not diff at all points u can see one notch at top point 
so clearly rolles have not been contradicted this way 
@allank

allank · Answer

Thanks @RajshikharGupta . I guess the examiner wanted the question to be puzzling.

anonymous · Answer

no it was an easy one