f(x) = xcos(x), 0

Question

f(x) = xcos(x), 0<x<pi
@ x=a, there is a local maximum
@ x=b, there is a point of inflextion

Sketch the graph, roughly indicating a and b. (done)

Find the value of a and b (using differentiation).

anonymous · Answer

Can you show your graph?

hartnn · Answer

know the product rule of differentiation ?

anonymous · Answer

yes, but then i'm getting tanx = 1/x. How do you solve that??

anonymous · Answer

http://fooplot.com/#W3sidHlwZSI6MCwiZXEiOiJ4KmNvcyh4KSIsImNvbG9yIjoiIzAwMDAwMCJ9LHsidHlwZSI6MTAwMCwid2luZG93IjpbIjAiLCIzLjE0IiwiLTQiLCIzIl19XQ--

hartnn · Answer

you can only solve that numerically...no standard method...
maybe @amistre64 or @jim_thompson5910 can help here...

anonymous · Answer

Anyone found a non numerical method yet? Or is it a complete no-no?

hartnn · Answer

@experimentX

experimentx · Answer

i don' think it has any answer in elementary terms .. so numerically done

experimentx · Answer

using x=pi/6 and ... and knowing tan(x) > x for x in 0 to pi/2 allows you to predict x is between pi/6 and 1.

using the same inequality, you approximate the values of x=b in that region.