f (x)>0: increasing f (x)<0: decreasing Solve the derivative inequality on the function’s domain. Split intervals at excluded values. In the sketch, the function is increasing for x<a or x>c, and decreasing for a<x<c. The derivative is zero at x=a and x=c. Changing gradient f (x)>0: gradient increasing f (x)<0: gradient decreasing

\(\mathrm{f}^{\prime}(x)>0:\ \text{increasing}\qquad \mathrm{f}^{\prime}(x)<0:\ \text{decreasing}\)

Solve the derivative inequality on the function’s domain. Split intervals at excluded values.

In the sketch, the function is increasing for \(x<a\) or \(x>c\), and decreasing for \(a<x<c\). The derivative is zero at \(x=a\) and \(x=c\).

\(\mathrm{f}^{\prime\prime}(x)>0:\ \text{gradient increasing}\qquad \mathrm{f}^{\prime\prime}(x)<0:\ \text{gradient decreasing}\)

Increasing and Decreasing Functions

Increasing and Decreasing Functions

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