Determine the interval of the function where the graph is increasing or decreasing
I guess that would be everywhere except where the tangent is horizontal.
To determine the interval of a function where the graph is increasing or decreasing, you need to find the intervals where the derivative of the function is positive or negative, respectively. Here's how you can do it step by step:
1. Find the derivative of the function. Let's say you have a function y = f(x), then the derivative is denoted as f'(x) or dy/dx.
2. Set up the derivative equation f'(x) = 0 and solve for x. The values of x where the derivative is zero or does not exist are called critical points.
3. Create a number line and place the critical points on it, including the endpoints of the given interval.
4. Choose test points within each interval between the critical points.
5. Evaluate the derivative at each test point. If the derivative is positive, then the function is increasing in that interval. If the derivative is negative, then the function is decreasing in that interval.
6. Finally, list the intervals where the function is increasing or decreasing based on the signs of the derivatives.
It is essential to note that the intervals where the function is increasing or decreasing are strictly based on the sign of the derivative. The actual function values may vary within those intervals.
By following these steps, you will be able to determine the intervals where the graph of the function is increasing or decreasing.