Understanding Decreasing Functions and their Derivatives | Exploring the Negative Slope and Rate of Change

If f(x) is decreasing, then f'(x) is?

If a function f(x) is decreasing, it means that as x increases, the corresponding values of f(x) are getting smaller

If a function f(x) is decreasing, it means that as x increases, the corresponding values of f(x) are getting smaller. In other words, the slope of the graph of f(x) is negative.

The derivative f'(x) of a function f(x) represents the rate at which the function is changing at each point x. It measures the slope of the tangent line to the graph of f(x) at that specific point.

When f(x) is decreasing, the derivative f'(x) will be negative. This is because a negative slope indicates a downward direction. Therefore, f'(x) < 0 when f(x) is decreasing.

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