The closed interval method is a way to solve a problem within a specific interval of a function. The solutions found by the closed interval method will be at the absolute maximum or minimum points on the interval, which can either be at the endpoints or at critical points.

The **closed interval method** is a way to solve a problem within a specific **interval** of a function. The solutions found by the **closed interval method** will be at the absolute maximum or minimum points on the **interval**, which can either be at the endpoints or at critical points.

Similarly, how do you find intervals? In determining **intervals** where a function is increasing or decreasing, you first **find** domain values where all critical points will occur; then, test all **intervals** in the domain of the function to the left and to the right of these values to determine if the derivative is positive or negative.

Moreover, what does Rolle’s theorem tell us?

**Rolle’s theorem** states that if a function f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b) such that f(a) = f(b), then f′(x) = 0 for some x with a ≤ x ≤ b.

How do you find the critical points of a function?

To find these **critical points** you must first take the derivative of the **function**. Second, set that derivative equal to 0 and solve for x. Each x value you find is known as a **critical** number. Third, plug each **critical** number into the original equation to obtain your y values.

### What is a first derivative?

The first derivative primarily tells us about the direction the function is going. That is, it tells us if the function is increasing or decreasing. The first derivative can be interpreted as an instantaneous rate of change. The first derivative can also be interpreted as the slope of the tangent line.

### How do you find a point of inflection?

Summary 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. In other words, solve f ” = 0 to find the potential inflection points. Even if f ”(c) = 0, you can’t conclude that there is an inflection at x = c.