How to calculate the point of inflexion of a curve?
Answers
Answered by
4
⭐HEYA FRIEND
Let me suggest you two methods. If you are comfortable with the calculus, select the calculus method. If you prefer to keep your math work in algebra, try the other. Both are easy.
⭐Calculus method⭐
Take the second derivative of the normal curve function.
Set the result equal to zero and solve the equation for the x-values of the critical points. (y-values of points are found by substituting the x-value in the original equation and solving for y)Take each of the one or more critical points which result and find the y-value for a convenient x-value on either side of it.
Any critical point where concavity is different on one side from the other (positive y-value result on one side, negative on the other) is a point of inflection.
⭐Algebra method⭐
The points of inflection for the standard normal distribution, whose mean = 0 and standard deviation = 1, has two inflection points, at x=1 and x=-1.
For any normal curve, then, the x-values for the points of inflection are found by subtracting the standard deviation from the mean and adding the standard deviation to the mean to get the two x values for the points of inflection.
As usual, find the y-value, if desired, by substituting these x-values in the normal curve equation in which you have substituted your particular mean and standard deviation.
⭐HOPE YOU UNDERSTAND AND IT WILL HELP YOU
⭐MARK IT IF YOU LIKE
⭐THANKS
Let me suggest you two methods. If you are comfortable with the calculus, select the calculus method. If you prefer to keep your math work in algebra, try the other. Both are easy.
⭐Calculus method⭐
Take the second derivative of the normal curve function.
Set the result equal to zero and solve the equation for the x-values of the critical points. (y-values of points are found by substituting the x-value in the original equation and solving for y)Take each of the one or more critical points which result and find the y-value for a convenient x-value on either side of it.
Any critical point where concavity is different on one side from the other (positive y-value result on one side, negative on the other) is a point of inflection.
⭐Algebra method⭐
The points of inflection for the standard normal distribution, whose mean = 0 and standard deviation = 1, has two inflection points, at x=1 and x=-1.
For any normal curve, then, the x-values for the points of inflection are found by subtracting the standard deviation from the mean and adding the standard deviation to the mean to get the two x values for the points of inflection.
As usual, find the y-value, if desired, by substituting these x-values in the normal curve equation in which you have substituted your particular mean and standard deviation.
⭐HOPE YOU UNDERSTAND AND IT WILL HELP YOU
⭐MARK IT IF YOU LIKE
⭐THANKS
Answered by
0
i don't know even a single .....above seems crrct...
Similar questions