What is a saddle point?
Coming from one direction it looks like we've hit a maximum, but from another direction is looks like we've hit a minimum.
Here are 3 graphs:
graph{y = x^4 [-12.35, 12.96, -6.58, 6.08]}
graph{-x^2 [-12.35, 12.96, -6.58, 6.08]}
graph{x^3 [-12.35, 12.96, -6.58, 6.08]}
Coming from the left it looks like a maximum, but coming from the right it looks like a minimum.
Here's one more for comparison:
graph{-x^5 [-10.94, 11.56, -5.335, 5.92]}
By signing up, you agree to our Terms of Service and Privacy Policy
A saddle point is a critical point of a function where the gradient is zero but it's not a local minimum or maximum. In other words, it's a point where the function stops increasing or decreasing along one direction but continues along another. At a saddle point, the function resembles a saddle shape in the vicinity of 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.
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 inverse of #y=log_2(x+4)#?
- How do you determine if #f(x)=x^6-9x^4+5x^2# is an even or odd function?
- What is the inverse function of #f(x) = 3 - 1/2x#?
- How do you determine whether a function is odd, even, or neither: #f(x)= (2x)/absx #?
- How do you identify all asymptotes or holes for #f(x)=(x^2-9)/(3x+3)#?

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