I study with a parametric equation like y=(a-b/x)-(u/x-c), x is the variable and i want to know its maximum or minimum value. Hovewer, when i take derivative of this function wrt x, i cannot find x because the equation does not have a simple form. Is there a way to find maximum or minimum value of such kind of a function? Thanks in advance

Thanks but it is not the fuction i study, i give it just as an example. My function is more complex than this one.

(double)

You might look at pre-transforms for x or post-transforms for y that can simplify the equation or it's derivative.

Don't know why it is called a parametric function; normally x = x(t) and y = y(t). anyways..What is the interval in which to find the max? It looks like blow-out at x = 0??Have you tried Brent's method? BTW it is deriivative-free!

QuoteOriginally posted by: Traden4AlphaYou might look at pre-transforms for x or post-transforms for y that can simplify the equation or it's derivative.Some methods don't need derivatives. R.P. Brent (1973). Algorithms for Minimization without Derivatives, Chapter 4. Prentice-Hall, Englewood Cliffs, NJ. ISBN 0-13-022335-2.

QuoteOriginally posted by: CuchulainnQuoteOriginally posted by: Traden4AlphaYou might look at pre-transforms for x or post-transforms for y that can simplify the equation or it's derivative.Some methods don't need derivatives. R.P. Brent (1973). Algorithms for Minimization without Derivatives, Chapter 4. Prentice-Hall, Englewood Cliffs, NJ. ISBN 0-13-022335-2.Nice!I'd imagine that one can also find the extrema of f by constructing the inverse of f, x = f'(y), and finding the range of y values over which f' is defined in x.

QuoteOriginally posted by: Traden4AlphaQuoteOriginally posted by: CuchulainnQuoteOriginally posted by: Traden4AlphaYou might look at pre-transforms for x or post-transforms for y that can simplify the equation or it's derivative.Some methods don't need derivatives. R.P. Brent (1973). Algorithms for Minimization without Derivatives, Chapter 4. Prentice-Hall, Englewood Cliffs, NJ. ISBN 0-13-022335-2.Nice!I'd imagine that one can also find the extrema of f by constructing the inverse of f, x = f'(y), and finding the range of y values over which f' is defined in x.Do you have an interesting example I could try?outrun,What do you do with CD?

QuoteOriginally posted by: CuchulainnQuoteOriginally posted by: Traden4AlphaQuoteOriginally posted by: CuchulainnSome methods don't need derivatives. I'd imagine that one can also find the extrema of f by constructing the inverse of f, x = f'(y), and finding the range of y values over which f' is defined in x.Do you have an interesting example I could try?Hmmm.... I've not thought about this for a while. What do you think of y = (c^N - x^N)^(1/N), with N not an odd number?

QuoteOriginally posted by: Traden4AlphaQuoteOriginally posted by: CuchulainnQuoteOriginally posted by: Traden4AlphaQuoteOriginally posted by: CuchulainnSome methods don't need derivatives. I'd imagine that one can also find the extrema of f by constructing the inverse of f, x = f'(y), and finding the range of y values over which f' is defined in x.Do you have an interesting example I could try?Hmmm.... I've not thought about this for a while. What do you think of y = (c^N - x^N)^(1/N), with N not an odd number?So, you want max(f(x)) and the x that produces it? or the other way around? In which interval?

QuoteOriginally posted by: CuchulainnQuoteOriginally posted by: Traden4AlphaQuoteOriginally posted by: CuchulainnQuoteOriginally posted by: Traden4AlphaQuoteOriginally posted by: CuchulainnSome methods don't need derivatives. I'd imagine that one can also find the extrema of f by constructing the inverse of f, x = f'(y), and finding the range of y values over which f' is defined in x.Do you have an interesting example I could try?Hmmm.... I've not thought about this for a while. What do you think of y = (c^N - x^N)^(1/N), with N not an odd number?So, you want max(f(x)) and the x that produces it? or the other way around? In which interval?Good question. Assume that all you want to know is the real y_max over all x and the real y_min over all xAnother simple function might be y = sin(c*sin(x))