Function is decreasing
First derivative less than zero
When we say a function is decreasing, we mean that the output values of the function decrease as the input values increase. This means that as we move to the right on the graph of the function, the height of the graph decreases.
We can also look at the slope of the function to determine if it is decreasing. If the slope of the function is negative, then the function is decreasing. In other words, the function is getting smaller as the input value increases.
For example, consider the function f(x) = -2x + 5. The slope of this function is -2, which is negative. Therefore, the function is decreasing. As x increases, the value of the function becomes smaller.
In terms of applications, a common example of a decreasing function is depreciation. If we have an asset like a car or a piece of equipment, its value decreases over time. We can model this situation with a decreasing function.
More Answers:
Mastering Parabolas: the Components, Equations, and Real-World ApplicationsDiscovering Relative Maximums in a Function using the First and Second Derivative Tests
Horizontal Tangent Lines: Their Role in Calculus and Maximizing/Minimizing Functions.