Negative Derivatives In Calculus: Identifying Decreasing Functions And Local Maximums

negative derivative means the

function is decreasing

In calculus, the derivative is the rate of change of a function with respect to its input variable. If a derivative is negative, it means that the function’s output is decreasing as the input variable increases. In other words, the function is decreasing over the interval in question.

For example, let’s consider the function f(x) = -2x + 5. The derivative of this function is -2, which is a negative value. This means that as x increases, the value of the function f(x) is decreasing. We can also think of it as the slope of the tangent line to the graph of the function being negative.

Negative derivatives are important in calculus because they can help us identify maximum points of a function. When a function is increasing and then starts to decrease, its derivative changes from positive to negative. The point where this happens is called a local maximum. Therefore, if we know the derivative of a function and it is negative at a certain point, we know that the function is decreasing at that point and we can look for local maximums.

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