Can You Find Inflection Points by Equating the Top Line of a Derivative to Zero?

[fran1942]

Hello, the following fraction is the derivative of a function:

(160-40t^2) / (t^2+4)^2

According to my textbook they have established the inflection points by equating the top line of this derived fraction to zero and then solving for x e.g. 160-40t^2 = 0. (t=+-2).

I was wondering is it a rule that you can simply equate the top line of a fraction format derivative to zero or am I missing something particular to this equation ?

Thanks for any clarification.

 

[chiro]

Hello, the following fraction is the derivative of a function:

(160-40t^2) / (t^2+4)^2

According to my textbook they have established the inflection points by equating the top line of this derived fraction to zero and then solving for x e.g. 160-40t^2 = 0. (t=+-2).

I was wondering is it a rule that you can simply equate the top line of a fraction format derivative to zero or am I missing something particular to this equation ?

Thanks for any clarification.

Hey fran1942.

What is the structure of your function? Is your derivative in terms of dy/dt = your expression in t or is dt/dx = expression in t?

 

[HallsofIvy]

Inflection points are points where the second derivative is 0, not the first derivative. It is true that a fraction is equal to 0 if and only if the numerator is 0.