Thread: Finding inflection points

Well, I am currently employing myself in finding the inflection points to the function y = 4x^2/(4-x^2). Through the process, the obtain the second derivative
y" = 32(4+3x^2)/(4-x^2)^3. I know from the definition of inflection points that x = -2 and x = 2 do not fit the criterion of being inflection points, and there are no real zeros; yet clearly, from the graph, I can see that there are changes in concavity. So are the two value, x = 2 and x = -2, pseudo points of inflection?

Point of inflection will occur when roots are repeated three times.

I.e. has a point of inflection at

has a point of inflection at

has a point of inflection at

and so on...

Originally Posted by Bashyboy

Well, I am currently employing myself in finding the inflection points to the function y = 4x^2/(4-x^2). Through the process, the obtain the second derivative
y" = 32(4+3x^2)/(4-x^2)^3. I know from the definition of inflection points that x = -2 and x = 2 do not fit the criterion of being inflection points, and there are no real zeros; yet clearly, from the graph, I can see that there are changes in concavity. So are the two value, x = 2 and x = -2, pseudo points of inflection?

the curve is concave down on and

the curve is concave up on

note that y is undefined at ... a curve cannot have inflection points where it is not defined. Inflection points are points defined on a curve where y'' changes sign.