## Where does the second derivative equal zero?

Inflection points

Inflection points are where the function changes concavity. Since concave up corresponds to a positive second derivative and concave down corresponds to a negative second derivative, then when the function changes from concave up to concave down (or vise versa) the second derivative must equal zero at that point.

## What does it mean if first and second derivative is 0?

When x is a critical point of f(x) and the second derivative of f(x) is zero, then we learn no new information about the point. The point x may be a local maximum or a local minimum, and the function may also be increasing or decreasing at that point.

**What does it mean if derivative is zero?**

Note: when the derivative curve is equal to zero, the original function must be at a critical point, that is, the curve is changing from increasing to decreasing or visa versa.

### What does it mean when the second derivative does not exist?

If the limit (f'(x+h)-f'(x))/h as h->0 is undefined anywhere in the domain then f’ is not differentiable, and we could say f” does not exist (or at least that no function is the second derivative of f everywhere in its domain).

### What happens if the first derivative is 0?

The first derivative of a point is the slope of the tangent line at that point. When the slope of the tangent line is 0, the point is either a local minimum or a local maximum. Thus when the first derivative of a point is 0, the point is the location of a local minimum or maximum.

**Where is the derivative zero?**

For what value(s) of x is the derivative zero? Answer: The sign of the derivative for the function is equal zero at the minimum of the function. The derivative is zero when x = 0.

#### Can an inflection point be zero?

An example of a stationary point of inflection is the point (0, 0) on the graph of y = x3. The tangent is the x-axis, which cuts the graph at this point. An example of a non-stationary point of inflection is the point (0, 0) on the graph of y = x3 + ax, for any nonzero a.

#### Can a point of inflection where the second derivative does not exist?

A point x=c is an inflection point if the function is continuous at that point and the concavity of the graph changes at that point. And a list of possible inflection points will be those points where the second derivative is zero or doesn’t exist.