negative derivative means the
Negative derivative means that the function is decreasing
Negative derivative means that the function is decreasing. In mathematics, the derivative of a function represents its rate of change at any given point. It tells us how the function is changing with respect to its input.
When the derivative is negative, it indicates that the function is decreasing. This means that as the input increases, the output of the function is getting smaller. In graphical terms, the function is sloping downward from left to right.
For example, consider a function f(x) = -2x + 3. If we take the derivative of this function, we get f'(x) = -2. The negative sign tells us that the function is decreasing. As x increases, the slope of the function is -2, meaning the function is becoming less positive or more negative.
Graphically, the function f(x) = -2x + 3 would be a straight line with a slope of -2. As x increases, the y-values decrease. So, if we evaluate the function at x = 0, f(0) = 3. But as x increases to, let’s say, x = 2, f(2) = -1. The output is smaller than the previous value, indicating that the function is decreasing.
In summary, a negative derivative means that the function is decreasing, and its output values are getting smaller as the input increases.
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