Is f(x)=1/x-1/x^3+1/x^5 increasing or decreasing at x=1?

1 Answer
Dec 7, 2015

I think is decreasing.

Explanation:

We can first evaluate the derivative of your function f'(x) which gives the inclination of your function; then we evaluate the derivative at x=1 to see if:
f'(1)>0 the function is increasing;
f'(1)<0 the function is decreasing;
f'(1)=0 the function has a minimum/maximum.

So:
f'(x)=-1/x^2+3/x^4-5/x^6

Evaluate it at x=1
f'(1)=-1+3-5=-3<0
the function is decreasing.

Graphically:
graph{(1/x)-(1/x^3)+(1/x^5) [-0.758, 4.11, -1.14, 1.292]}