How do you figure out the minimum and maximum for the graph of a function (without having a list of data, just looking at the graph?) Would you right both of the minimums (there's two points that are equally low), one of them or do something different? Thanks.
If the minimums were exactly the same, I would write the minimum of the functions was xxxx, and occured at x= and x= ...
To find the minimum and maximum points of a graph without having a list of data, you can use the concept of critical points. Critical points are the locations where the derivative of the function is either zero or undefined. These points often indicate potential minimum and maximum points on the graph.
Here's how you can proceed:
1. Identify the critical points: Find the points where the derivative of the function is zero or undefined. To do this, you need to know how to take the derivative of the given function. If you are unsure about the derivative, you can use online resources or consult a calculus textbook.
2. Check for endpoints: If the graph is limited by a specific range (e.g., from -∞ to +∞), then the minimum or maximum point may occur at the endpoints. Check whether the graph extends towards infinity or is bounded within a specific range.
3. Evaluate the function at the critical points and endpoints: Plug in the x-values from the critical points and endpoints into the original function to get the corresponding y-values.
4. Compare the y-values: Compare the y-values obtained in step 3. The highest y-value corresponds to the maximum point, and the lowest y-value corresponds to the minimum point. If there are multiple critical points with the same y-value, they would represent multiple minimum or maximum points with equal heights.
So, to answer your question, if there are multiple points with the same lowest y-value (two or more equally low points), you should write all of them as the minimum points.
Remember, this method assumes that the graph is continuous and differentiable. If the graph has sharp corners, cusps, or vertical asymptotes, this approach might not accurately identify the minimum and maximum points.