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AT POINT OF INFLECTION THE DERIVATIVE MUST BE ZERO CORRECT?? AND HOW CAN A POINT OF INFLEXION BE IDENTIFIED ON A GRAPH OF FUNCTION AND WAT DOES F DOUBLE DERIVATIVE X ESIXT MEAN???
Dear Mir First derivative need not to be zero.Pint of inflection can be identified where there is change of curvature.Since the first derivative is at an extremum, it follows that the second derivative, f″(x), is equal to zero if it exists, but the latter condition does not provide a sufficient definition of a point of inflection. One also needs the lowest-order non-zero derivative to be of odd order (third, fifth, etc.). If the lowest-order non-zero derivative is of even order, the point is not a point of inflection. All the best. AKASH GOYAL AskiitiansExpert-IITD Please feel free to post as many doubts on our discussion forum as you can. We are all IITians and here to help you in your IIT JEE preparation. Win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian. Now you score 5+15 POINTS by uploading your Pic and Downloading the Askiitians Toolbar respectively : Click here to download the toolbar..
Dear Mir
First derivative need not to be zero.Pint of inflection can be identified where there is change of curvature.Since the first derivative is at an extremum, it follows that the second derivative, f″(x), is equal to zero if it exists, but the latter condition does not provide a sufficient definition of a point of inflection. One also needs the lowest-order non-zero derivative to be of odd order (third, fifth, etc.). If the lowest-order non-zero derivative is of even order, the point is not a point of inflection.
All the best.
AKASH GOYAL
AskiitiansExpert-IITD
Please feel free to post as many doubts on our discussion forum as you can. We are all IITians and here to help you in your IIT JEE preparation.
Win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian.
Now you score 5+15 POINTS by uploading your Pic and Downloading the Askiitians Toolbar respectively : Click here to download the toolbar..
how to identify inflection pt if second derivative is not defined, without drawing the graph. ex: the function 2x2/(x2 – 1). It is concave up when |x| > 1 and concave down when |x| < 1. However, it has no points of inflection because 1 and -1 are not in the domain of the function.
how to identify inflection pt if second derivative is not defined, without drawing the graph.
ex: the function 2x2/(x2 – 1). It is concave up when |x| > 1 and concave down when |x| < 1. However, it has no points of inflection because 1 and -1 are not in the domain of the function.
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