If the first derivative is negative at a point, then the function is decreasing at that point. If the first derivative is positive at a point, then the function is increasing at that point. Then, we can analyze its sign at different points in the interval to determine whether the function is increasing or decreasing. To use the first derivative test, we need to find the first derivative of the function. The first derivative test is a method used to determine whether a function is increasing or decreasing on a specific interval by analyzing the sign (positive or negative) of its first derivative.
In the graph above, the slope of the tangent line at each of the minima and maxima is zero, meaning the tangent line is horizontal.ĥ.3 Determining Intervals on Which a Function is Increasing or Decreasing Critical points are important in finding the extrema of a function, as local extrema will always occur at critical points (where the derivative is either 0 or undefined).
A critical point of a function f(x) is a value c in the domain of the function such that either f'(c) = 0 or f'(c) does not exist.
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