f'(x)<0
When f'(x) is less than 0, it means that the derivative of the function f(x) is negative
When f'(x) is less than 0, it means that the derivative of the function f(x) is negative. The derivative of a function represents its rate of change at any given point. In this case, a negative derivative indicates that the function is decreasing.
To understand this concept further, let’s consider an example:
Suppose we have a function f(x) = x^2. To find the derivative, we can use the power rule, which states that if f(x) = x^n, then f'(x) = n*x^(n-1).
In this case, the derivative of f(x) = x^2 would be f'(x) = 2*x^(2-1) = 2*x.
If we evaluate the derivative at a specific point, say f'(1), we would get f'(1) = 2*1 = 2.
Since f'(1) = 2, which is greater than 0, we can say that at x = 1, the function is increasing because the derivative is positive.
Now, if we take another point, say f'(-1), we would get f'(-1) = 2*(-1) = -2.
Since f'(-1) = -2, which is less than 0, we can say that at x = -1, the function is decreasing because the derivative is negative.
Therefore, when f'(x) is less than 0, it means that the function is decreasing at that particular point.
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