What does d2ydx2 mean

If the second derivative is positive at a critical point, then the critical point is a local minimum. The second derivative will be zero at an inflection point. Furthermore, is second derivative acceleration?

The second derivative is the rate of change of the rate of change of a point at a graph the "slope of the slope" if you will. This can be used to find the acceleration of an object velocity is given by first derivative.

An inflection point is a point on the graph of a function at which the concavity changes. Points of inflection can occur where the second derivative is zero. The second derivative of a function f measures the concavity of the graph of f. A function whose second derivative is positive will be concave up also referred to as convex , meaning that the tangent line will lie below the graph of the function.

What happens if the second derivative is 0? A positive second derivative corresponds to a function being concave up, and a negative corresponds to concave down, so it makes sense that it is when the second derivative is 0 that our function is changing concavity, and hence corresponds to an inflection point.

When can you not use the second derivative test? If f' x doesn't exist then f" x will also not exist, so the second derivative test is impossible to carry out. It only takes a minute to sign up. Connect and share knowledge within a single location that is structured and easy to search. Okay this may sound stupid but I need a little help You can apply this operator to a differentiable function. And you get a new function.

Do you have any concrete examples for which you need to calculate these two? It would probably make it more easy to grasp for you if I could explain it in a few examples. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. Ask Question. Asked 8 years, 7 months ago.

Its value at a point on the function gives us the slope of the tangent at that point. This is because, by definition, the derivative gives the slope of the tangent line. Horizontal lines have a slope of zero. Therefore, when the derivative is zero, the tangent line is horizontal. A horizontal line has slope zero since it does not rise vertically i. Since there is an inverse relation between r and Y the IS curve is downward sloping from left to right.