I think you may be misinterpreting what it says. It is strangely worded. Better would be "f'(x)=1-sin(x), which is ≥0 since sin(x)≤1 for any real x".quicksilver123 said:
Maxima minima on an interval refers to the highest and lowest values of a function or graph over a specific interval. It represents the maximum and minimum points on the graph within a given interval.
To calculate Maxima minima on an interval, you need to take the derivative of the function and set it to zero. Then, solve for the x-values that make the derivative equal to zero. These x-values represent the critical points, which can be used to determine the maxima and minima on the interval.
Finding Maxima minima on an interval is important because it helps us understand the behavior of a function over a specific range. It can also provide valuable information about the function, such as its increasing and decreasing intervals, and the location of maximum and minimum values.
Yes, Maxima minima on an interval can be negative. It simply means that the function has a negative value at that point, and it is the minimum value within the given interval. Similarly, a positive Maxima minima on an interval would indicate the maximum value of the function within the interval.
Trigonometry is often used in calculus to study the behavior of functions, including finding the Maxima minima on an interval. Trigonometric functions, such as sine and cosine, can have maximum and minimum values within a given interval, and their derivatives can help us determine these values.