Hi all

İ have an equation like r(x)=1-x^2.

İs it possible to find max value of function.

Regards

Hi Seçkin. Some notes about finding maxs.

maximun.sm (19,07 KiB) descargado 1525 vez(es).

Best regards.
Alvaro.

Hi Ronazar thanks for your answer.

İs it possible to find inverse of max value

For example f(5)=2 ise inverse of 2 equals 5

Thanks

Wrote

Ä°s it possible to find max value of function.

The derivative method is just a quick lazy approach for convenience.
Derivative operator is symbolic, thus won't work for spline interpolation.
The min/max general method is the Golden Ratio.
You are confused with your next question "inverse"
An InverseFunction is a function that solve the given f(x)
... in preparation
Visit Golden ration posted next few minutes

Cheers.

Wrote

Ä°s it possible to find inverse of max value
For example f(5)=2 ise inverse of 2 equals 5

... Sorry: don't understand your maths in there.
1. Understand InverseFunction
2. ISA altitude as superb application [won't find in Web]

Solve Inverse Symbolic Suite.sm (93,66 KiB) descargado 1303 vez(es).
Inst_ISA [Landing altitude PDF].sm (305,35 KiB) descargado 1120 vez(es).

Wrote

Hi Ronazar thanks for your answer.

İs it possible to find inverse of max value

For example f(5)=2 ise inverse of 2 equals 5

Thanks

Hi. If you have a max of y=2 that happen for x=5, then you can't invert y=f(x) near x=5, because then x=5 it's a critical point, then you have f'(5)=0, or a limit of the interval or a discontinuity, and the inverse function theorem it's a local theorem and needs f'(x)≠0 in the study interval.

Notice that the inverse function theorem it's easy to see graphically (the function isn't one to one), but very hard to demonstrate, as you can see at: http://people.math.sc.edu/schep/InversefunctionThm.pdf

Best regards.
Alvaro.

Revisit your example. The mechanics of Inversing a function is intuitive.
However the maths under the hood belongs to few advanced CAS [Maple World top].
Mathematica will do same, most of the times of different presentation.
Before you do anything with a function => graph.
Please, do not hesitate for more.