What are the points of inflection, if any, of #f(x) =(x+4)/(x-2)^2#?
The second derivative must vanish in order for the function to have an inflection point.
Determine the second derivative by:
By signing up, you agree to our Terms of Service and Privacy Policy
To find the points of inflection, we first need to find the second derivative of the function and then determine where it changes sign.
The first derivative of ( f(x) ) is ( f'(x) = \frac{-2x^2 - 4x + 16}{(x - 2)^3} ).
The second derivative is ( f''(x) = \frac{2x^3 - 4x^2 - 32x + 48}{(x - 2)^4} ).
To find the points of inflection, we need to find where ( f''(x) = 0 ) or does not exist, and then check the sign of ( f''(x) ) around those points.
Solving ( f''(x) = 0 ) gives us ( x = 2 ).
At ( x = 2 ), the second derivative changes sign from negative to positive, indicating a point of inflection.
Therefore, the point of inflection of the function ( f(x) = \frac{x+4}{(x-2)^2} ) is at ( x = 2 ).
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.
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.
- How do you find the inflection points for the function #f(x)=x^3+x#?
- The area of the region bounded by the curve y=x^2 and y=4x-x^2 is ?
- How do you determine whether the function #f(x)=x^8(ln(x))# is concave up or concave down and its intervals?
- How do you find the relative extrema for #f(x)=x^4# ?
- A particle moves according to the equation #s=1-1/t^2#, how do you find its acceleration?

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