Understanding the Concept of dy/dx < 0 | How a Negative Derivative Indicates Decreasing y as x Increases

When dy/dx < 0 as x increases...

When dy/dx < 0 as x increases, it means that the derivative of y with respect to x is negative, indicating that y is decreasing as x increases

When dy/dx < 0 as x increases, it means that the derivative of y with respect to x is negative, indicating that y is decreasing as x increases. In other words, the slope of the function y with respect to x is negative. To understand this concept better, let's consider an example. Suppose we have a function y = f(x), and its derivative dy/dx is negative for increasing values of x. This implies that as x increases, the rate of change of y with respect to x is negative. This can be visualized as a downward slope or a decreasing trend on a graph. For instance, let's say we have a linear function y = 2x. Its derivative is dy/dx = 2, which is a positive constant. In this case, as x increases, y also increases, and the slope of the function remains constant. However, if the function were y = -2x, the derivative would be dy/dx = -2, which is negative. As x increases, y decreases, and the function exhibits a downward slope. In summary, when dy/dx < 0 as x increases, it indicates that the function y is decreasing and has a negative slope as x increases.

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