Understanding Increasing and Decreasing Behavior of a Function | A Step-by-Step Guide

Looking at a graph of f(x)… how do you know where F(x) is increasing/decreasing?

To determine where the function F(x) is increasing or decreasing, you need to look at the slope of the graph

To determine where the function F(x) is increasing or decreasing, you need to look at the slope of the graph. When the slope is positive, the function is increasing, and when the slope is negative, the function is decreasing.

Here are the steps to identify where F(x) is increasing or decreasing:

1. Find the derivative of F(x): The derivative measures the rate of change of a function. If F(x) is given as an equation, you can find its derivative using differentiation rules.

2. Set the derivative equal to zero: Set the derivative equation equal to zero and solve for x. The values of x obtained will be the critical points of F(x), where the function may change from increasing to decreasing, or vice versa.

3. Determine the intervals: Divide the number line into intervals based on the critical points found in step 2. Each interval represents a different behavior of the function.

4. Test a point in each interval: Choose a value of x within each interval and substitute it into the derivative equation obtained in step 1. If the derivative is positive, the function is increasing in that interval. If the derivative is negative, the function is decreasing in that interval.

By following these steps, you can determine where the function F(x) is increasing or decreasing based on the given graph or equation.

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