What Are the Maximum and Minimum Values of y When x^3 is 8+- 2(14)^1/2?

[PhysicoRaj]

In the first line of the image in post #21, while finding the second derivative, you have written -2x instead of y^2-2x

 

[Liang Wei]

Erm I have found my mistakes and able to show it but an additional question is can I use the sign test to find the maximum and minimum values from this kind of equation?sorry to bother you and thanks.

 

[PhysicoRaj]

can I use the sign test to find the maximum and minimum values from this kind of equation?

You mean the second derivative test? It says only if the point is maxima or minima. It doesn't give you the value.

 

[Liang Wei]

Sign test is a test which you use a value which lies inside the interval of a variable,example x then substitute it into dy/dx to find the sign and we can find the maxima and minima.but anyways I manage to prove it by using 2nd derivative but not sure correct or wrong.

 

[PhysicoRaj]

Sign test is a test which you use a value which lies inside the interval of a variable,example x then substitute it into dy/dx to find the sign and we can find the maxima and minima.

Oh that one, for that you need to know the interval, and it requires you to solve for x.

but anyways I manage to prove it by using 2nd derivative but not sure correct or wrong.

Correct as long as you don't assume the values of x with a calculator and as long as y has both maxima and minima.

 

[Liang Wei]

Ok thanks