If f(x) is decreasing, then f'(x) is?
If f(x) is a function that is decreasing, it means that as the input value of x increases, the corresponding output values of f(x) are decreasing
If f(x) is a function that is decreasing, it means that as the input value of x increases, the corresponding output values of f(x) are decreasing. In other words, as we move from left to right along the x-axis, the values of f(x) are getting smaller.
The derivative, f'(x), represents the rate of change of the function f(x) with respect to x. It gives us information about how the function is changing at any given point.
If f(x) is decreasing, it means that as x increases, the values of f(x) are getting smaller. This implies that the slope of the graph of f(x) is negative. The derivative, f'(x), gives us the slope of the tangent line to the graph of f(x) at any point.
Therefore, if f(x) is decreasing, it implies that the derivative, f'(x), is negative, indicating that the function is decreasing at that particular point. Mathematically, we can express this as:
f(x) is decreasing if and only if f'(x) < 0 So, when a function is decreasing, its derivative f'(x) is negative.
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