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

Find the first derivative , then determine if it is *positive* (increasing) or *negative* (decreasing) at

Using the quotient rule , then simplify ...

Now,

So, at

Hope that helped

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

To determine whether ( f(x) = \frac{{(x - 2)^2}}{{x - 1}} ) is increasing or decreasing at ( x = 2 ), we need to analyze the sign of the derivative of the function at that point.

First, find the derivative of ( f(x) ): [ f'(x) = \frac{{2(x - 2)(x - 1) - (x - 2)^2}}{{(x - 1)^2}} ]

Now, evaluate ( f'(2) ) to determine the behavior of the function at ( x = 2 ): [ f'(2) = \frac{{2(2 - 2)(2 - 1) - (2 - 2)^2}}{{(2 - 1)^2}} ] [ f'(2) = \frac{{2(0)(1) - 0}}{{1}} ] [ f'(2) = 0 ]

Since the derivative ( f'(2) ) is zero, we cannot determine whether the function is increasing or decreasing at ( x = 2 ) using the first derivative test. Additional analysis may be required, such as considering the behavior of the function around the point ( x = 2 ).

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

- What are the critical values, if any, of # f(x)= sin|x|#?
- Is #f(x)=(x^3+2x^2-x-2)/(x+3)# increasing or decreasing at #x=-2#?
- Is #f(x)=(x+7)(x-2)(x-1)# increasing or decreasing at #x=-1#?
- How do you find the critical numbers of #f(x) = x^4(x-1)^3#?
- Is #f(x)=-x^3+3x^2-x+2# increasing or decreasing at #x=-1#?

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