# What are the points of inflection, if any, of #f(x)=1/x #?

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

To find the points of inflection of ( f(x) = \frac{1}{x} ), we first need to find the second derivative, ( f''(x) ).

( f(x) = \frac{1}{x} ) ( f'(x) = -\frac{1}{x^2} )

Using the power rule for differentiation, we find: ( f''(x) = 2 \frac{1}{x^3} )

To find the points of inflection, set the second derivative equal to zero and solve for ( x ): ( 2 \frac{1}{x^3} = 0 ) ( \frac{1}{x^3} = 0 )

There are no real solutions to this equation. Hence, there are no points of inflection for the function ( f(x) = \frac{1}{x} ).

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.

- How do you find the inflection point of a logistic function?
- Is #f(x)=3x^5-x^3+8x^2-x+3# concave or convex at #x=-4#?
- What are the points of inflection, if any, of #f(x) = 4x^6 +4x^5 -5x^4 #?
- What is the second derivative of the function #f(x) = (x) / (x - 1)#?
- How do you find the antiderivative of #x^2+5x#, if the point (0,5) exists on the graph of the antiderivative?

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