appplejack said:
appplejack said:
An increasing function is a mathematical function where the output values increase as the input values increase. In other words, as the independent variable increases, the dependent variable also increases.
To determine if a function is increasing or decreasing, you can look at the graph of the function. If the graph is moving from left to right and going upwards, then the function is increasing. If the graph is moving from left to right and going downwards, then the function is decreasing.
A local maximum or minimum is a point on the graph of a function where the function reaches its highest or lowest value in a specific interval. It is also known as a relative maximum or minimum, as it is only the highest or lowest point within a particular range.
No, a function cannot be both increasing and decreasing. A function can either be increasing, where the output values increase as the input values increase, or decreasing, where the output values decrease as the input values increase.
To find the intervals where a function is increasing or decreasing, you can use the first derivative test. If the first derivative of the function is positive, then the function is increasing. If the first derivative is negative, then the function is decreasing. The points where the first derivative is equal to zero are the local maximum or minimum points.