Question

Find the local maximum(s) and local minimum(s) of f(x) = cos (1/x) on the interval 1/3π , 1/π .

Answer 1

The graph for defined region from 1/3pi to 1/pi or (0.1061 to 0.3183) is given below,

From graph it is clear that at 1/3pi and 1/pi local maximum occur and at 1/2pi local maximum occur.

Also, f'(x) = sin(1/x)*(-1/x^2) = 0.

sin(1/x) = 0,

This gives, x = 1/3pi, 1/2pi and 1/pi.

So, these are the point where maxima or minima occur.

And, the local maxima value is 1 at 1/2pi.

And, the local minima value is -1 at 1/3pi and also at, 1/pi.