Final answer:
To determine if a graph is increasing or decreasing on a calculator, check for positive or negative values of the derivative, identify critical points, and analyze the slope of the tangent line. The slope value signifies whether the graph is ascending or descending as the x-value rises or falls.
Step-by-step explanation:
To determine where the graph of a function is increasing or decreasing using a calculator, one can use several methods:
- Look for positive and negative values of the derivative: If you can calculate the derivative of the function, then where the derivative is positive, the graph is increasing, and where it is negative, the graph is decreasing.
- Examine the concavity of the graph: While this can give some information about the behavior of the graph, it is not directly related to increasing or decreasing intervals.
- Identify critical points: Critical points occur where the derivative is zero or undefined, and they can indicate potential locations where the graph changes from increasing to decreasing or vice versa.
- Analyze the slope of the tangent line: This is essentially the same as looking at the derivative, as the slope of the tangent line at any point is given by the derivative at that point.
The slope value of a graph is indicative of its behavior. A positive slope means the graph is increasing as the x-value increases, and a negative slope means the graph is decreasing. To translate the equation of a line in terms of slope and intercept, one can manipulate the line to change its slope or intercept, compute and interpret growth rates, and then read and manipulate the graph accordingly.