x^3 -6x^2 +12x +18
Which one of these choices are correct( Choose A,B,C OR D only)
A. X=2 is a point of inflection
B. X=2 is an upward turning point and x=0 is a downward turning point
C. X=2 is a downward turning point and x=0 is a upward turning point
D. X=2 can not be characterised because f’’(x)=0
The graph are below: Showing the point at X=2
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Thanks a lot for answering the question.
I still believe that it is necessary to show that f''(x) changes sign at x = 2 to confirm a point of inflection.
I can't say for sure that there is not some function that exists where f'(a) = 0, f''(a) = 0 , has no extrema at (a,f(a)) , and that does not have an inflection point at x = a ... I just can't think of a rigorous proof of your statement or a suitable counterexample.