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.

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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]

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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.