How would the graph of f look like at a specific point if that point has an undefined concavity, but defined at f?
Pictures would be nice, but explanations and description is alright.
Or is is even possible?
Thank you.
Pictures would be nice, but explanations and description is alright.
Or is is even possible?
Thank you.
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This could be a discontinuous piece function where the first and second derivative do not exist because the left side and right side do not converge on the same value, even though the function is defined at a point.
Also, it could be a function like y = |x^2-4| where the function is continuous, but there is a sharp turn,so the first and second derivative do not exist at the turning point.
Hoping this helps!
Also, it could be a function like y = |x^2-4| where the function is continuous, but there is a sharp turn,so the first and second derivative do not exist at the turning point.
Hoping this helps!
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If there is an undefined concavity this either means 1 of 2 things, either you are misjudging that point on the graph or you are looking at an inflection point, which means that the concavity is changing but to find out if the concavity is positive, negative or changing YOU HAVE TO LOOK AT (f prime), because you cant judge it from the graph of f, I mean you could but it would be extremely difficult. Also if on the graph of f prime the concavity is changing from positive -> negative, you will have a local max on the graph of f double prime, but if concavity is changing from negative -> positive you will have a local min on the graph of f double prime... hope I didnt confuse you, hope this'll help