Find the critical values and determine the intervals where f

Find the critical values and determine the intervals where f(x) is increasing and f(x) is decreasing if f(x)= 1 + (3/x) +(2/ x^2)

Solution : Differentiate the given function, we get

f\'(x)=0-(3/x^2)-4/x^3

For critical values, f\'(x)=0

-3/x^2-4/x^3=0

-3x-4=0

Or. x=-4/3. This is the critical value.

And the intervals are (-infinity , -4/3) and (-4/3, infinity )

Let x=-2, then f\'(2)=-3/4+4/8=-3/4+1/2=-3+2/4=-1/4.

Therefore the function is decreasing in the interval (-infinity, -4/3) and increasing in the interval (-4/3, infinity ).