Max of (sin(x))^(e^x)

[lrdheat]

When using fmax on this function in CAS or home, (sin(x))^(e^x), I get brackets. When using solve to find when the function equals 1, I get brackets. If I solve for function =.99, I get a suitable answer. Using d/dx of the function in solve to equal zero, I also get brackets. If I solve d/dx of the function to equal .01, I get suitable answers. Why the lack of success? In graphing app, extremums are found without difficulty.

[lrdheat]

The solution for d/dx may not be suitable...it should be closer to max of f(x) when solving for it to equal .001, yet it is further away! In fact, when plotting d/dx of the function, I get 2 diverging curves near the max of f(x). This on a tight plot from x=14.1324 to 14.142 .

[lrdheat]

It does plot d/dx fine...autoscale solved that misperception

[lrdheat]

SolveN on my CASIO fx-CG10 over the range of 14.1342 to 14.1424 succeeds in producing 9pi/2 on it's display for d/dx ((sin(x))^e^x).

[parisse]

If you are interested in approx. solutions, use fsolve.

Code:


f(x):=(sin(x))^(e^x);
fsolve(f(x)=1);
solve(f'(x)=0);

solve is for *exact* solving of polynomial-like equations, but this kind of equation f(x)=c is not solvable exactly for a generic second member c. solve will automatically switch to fsolve if there is an approx value inside.

[lrdheat]

Forgot about fsolve. Thanks!

[lrdheat]

Not at all arguing that the CASIO is better... with fsolve, an interval of 14.13 to 14.14 is still to wide for fsolve to find the solution to d/dx ((sin(x))^(e^x))=0. Solve on the CASIO fx-CG10 finds the answer with the much wider range of 13 to 15. (SolveN requires the much narrower range on the CASIO)

[parisse]

Not that surprising with your function, you are taking sin(x) to a power of more of 1 million. I wonder what kind of math problem you are solving.

[lrdheat]

Just messing around..

In my early early college days when slide rules were king, and the HP 35 emerged, it seemed miraculous. The guide book to the 35 remarked that this instrument was something like a Dick Tracy or Walter Mitty might be expected to carry. My peers and I wondered if symbolic math, graphing capabilities would ever be possible on a hand held device. It still astounds me...just amazing and wonderful.

Still have my best slide rules...

[Wes Loewer]

(02-26-2018 03:40 AM)lrdheat Wrote:  My peers and I wondered if symbolic math, graphing capabilities would ever be possible on a hand held device. It still astounds me...just amazing and wonderful.

I remember reading a book in late 70's or so that predicted that calculators would some day have small pen plotters underneath the calculator. To plot a graph, you would simply set the calculator on a piece of paper and it would plot a graph.

Quote:Still have my best slide rules...

Nothing fancy, but I still have an aluminum Picket N902-ES and a Concise 700-MM circular slide rule.