`f(x)=cos((pi)/(x)), x ne 0`, find the interval in which f(x) in increasing.

Let f'(sinx)lt0andf''(sinx)gt0,AAx in (0,(pi)/(2)) and g(x)=f(sinx)+f(cosx), then find the interval in which g(x) is increasing and decreasing.

Find the interval for which f(x)=x-sinx is increasing or decreasing.

Find the intervals in which f(x)=(x)/(log x) is increasing or decreasing

Find the intervals in which f(x)=(x)/(log x) is increasing or decreasing

Find the intervals in which f(x)=sin x-cos x, where ' 0

Let g(x)=f(log x)+f(2-log x) and f'(x)<0AA x in(0,3) Then find the interval in which g(x) increases.

Let f(x)={{:(xe^(ax)",", x le0),(x+ax^2-x^3",",x gt 0):} where a is postive constant . Find the interval in which f'(X) is increasing.

Write the interval in which f(x)=sin x+cos x,x in[0,pi/2] is increasing.

Consider a function fdefined by f(x)=sin^(-1)sin((x+sin x)/(2))AA x in[0,pi] which satisfies f(x)+f(2 pi-x)=pi AA x in[pi,2 pi] and f(x)=f(4 pi-x) for all x in[2 pi,4 pi] then If alpha is the length of the largest interval on which f(x) is increasing,then alpha=