# Maximum and minimum values

Oooo

PhysicoRaj
Gold Member
Yeah,the x values are from the x^3 that they provide,when you substitute those values,you will find that there are many zero values so it is able to get the d2y/dx2= +value which is greater than zero so both values of x are local minimums

Okay I see..
Go step by step: You found first derivative and equated it to zero. Implies y=x^2/2. Next step is to use this and solve for 'x'. See if you can do this by substituting in the givens.

I think they expect you to arrive at ##x^3=8+-2(14)^{1/2}## rather than assume it at the first. This is what is going wrong.

I don't think I know how do I get x^3=8+-2(14)^{1/2} from the equations provided

PhysicoRaj
Gold Member
I don't think I know how do I get x^3=8+-2(14)^{1/2} from the equations provided

I know, it is quite difficult. What you have done is right, but there are several doubts like:
>You used a calculator to approximate the given x value ( I think this is unfair).
>Both x values are yielding minima (right?)

Yup both x values are yielding minima,if I don't use the calculator,it would be really difficult to sub it into the 2nd derivative. It has took me several hours but I am still unable to work it out.

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

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
Gold Member
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.

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
Gold Member
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 dont assume the values of x with a calculator and as long as y has both maxima and minima.

Ok thanks