# Is #f(x)=1/(x-1)-1/(x+1)^2# increasing or decreasing at #x=0#?

Since

now use the chain rule:

By signing up, you agree to our Terms of Service and Privacy Policy

To determine if ( f(x) = \frac{1}{x-1} - \frac{1}{(x+1)^2} ) is increasing or decreasing at ( x = 0 ), we need to evaluate the sign of its derivative at that point.

The derivative of ( f(x) ) is ( f'(x) = \frac{-1}{(x-1)^2} + \frac{2}{(x+1)^3} ).

At ( x = 0 ), ( f'(0) = \frac{-1}{(-1)^2} + \frac{2}{(1)^3} = -1 + 2 = 1 ).

Since the derivative is positive at ( x = 0 ), the function ( f(x) ) is increasing at that point.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- What is the maximum value of #y=-3sinx+2#?
- Is #f(x)=x-1/sqrt(x^3-3x)# increasing or decreasing at #x=2#?
- What are the local extrema, if any, of #f (x) =sqrt(4-x^2)#?
- How do you find the critical points for # y = x^3 + 12x^2 + 6x + 8 #?
- What are the extrema of #f(x)=-sinx-cosx# on the interval #[0,2pi]#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7