## What is the 1st and 2nd derivative of a function?

In other words, just as the first derivative measures the rate at which the original function changes, the second derivative measures the rate at which the first derivative changes. The second derivative will help us understand how the rate of change of the original function is itself changing.

### What is the first derivative of a curve?

The first derivative of a function is an expression which tells us the slope of a tangent line to the curve at any instant. Because of this definition, the first derivative of a function tells us much about the function. If is positive, then must be increasing. If is negative, then must be decreasing.

#### What is the second derivative of a curve?

On the graph of a function, the second derivative corresponds to the curvature or concavity of the graph. The graph of a function with a positive second derivative is upwardly concave, while the graph of a function with a negative second derivative curves in the opposite way.

**How do you sketch a curved graph?**

The following steps are taken in the process of curve sketching:

- Domain. Find the domain of the function and determine the points of discontinuity (if any).
- Intercepts.
- Symmetry.
- Asymptotes.
- Intervals of Increase and Decrease.
- Local Maximum and Minimum.
- Concavity/Convexity and Points of Inflection.
- Graph of the Function.

**How do you read a second derivative graph?**

The second derivative tells whether the curve is concave up or concave down at that point. If the second derivative is positive at a point, the graph is bending upwards at that point. Similarly if the second derivative is negative, the graph is concave down.

## How do you draw a curve from a function?

### How do you draw a curved function?

#### How do you read the second derivative graph?

**How do you find the second derivative of a function?**

To find the second derivative, first we need to find the first derivative. The derivative of a natural log is the derivative of operand times the inverse of the operand. So for the given function, we get the first derivative to be . Now, we have to take the derivative of the first derivative.

**What is the second derivative test for critical points?**

The point x may be a local maximum or a local minimum, and the function may also be increasing or decreasing at that point. The three cases above, when the second derivative is positive, negative, or zero, are collectively called the second derivative test for critical points.

## What happens when the second derivative of f(x) is zero?

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.

### How to find the second derivative of a natural log?

To find the second derivative, first we need to find the first derivative. The derivative of a natural log is the derivative of operand times the inverse of the operand. So for the given function, we get the first derivative to be