Points of inflexion and stationary points.

I am finding the point
of inflexion by rearranging the d^2y/dx^2 = 0 to
find x and then plugging the number into the
original equation to find y which gives me one set
of co-ordinates for the point of inflexion.
But I think sometimes there can be more than
one point of inflexion, how do I find others please?

I am finding the point of inflexion by rearranging the d^2y/dx^2 = 0 to find x and then plugging the number into the original equation to find y which gives me one set of co-ordinates for the point of inflexion.

But I think sometimes there can be more than one point of inflexion, how do I find others please?

Then when you set dy/dx or $d^2y/dx^2$ equal to zero, you'll get a quadratic or qubic or quartic which you can then solve.

*Inflection & if the equation d2y/dx2 = 0 has one solution, then there is one point of inflection, if it has 3 solutions then it has 3 points of inflection etc.

Thank-you both for answering.





My d^2y/dx^2 was giving things like 6x-2

I am finding the point of inflexion by rearranging the d^2y/dx^2 = 0 to find x and then plugging the number into the original equation to find y which gives me one set of co-ordinates for the point of inflexion.

But I think sometimes there can be more than one point of inflexion, how do I find others please?