Question

c) using the graphs of f and f, indicate where f is increasing and decreasing. give your answer

note: when using interval notation in webwork, remember that:
you use inf for ∞ and -inf for −∞,
and use u for the union symbol.
enter dne if an answer does not exist.
f is increasing on (−∞,−2)∪(2,∞)
f is decreasing on (−2,2)

Explanation:

Step1: Recall derivative - increasing - decreasing relationship

If \(f^{\prime}(x)>0\), \(f(x)\) is increasing. If \(f^{\prime}(x)<0\), \(f(x)\) is decreasing.

Step2: Analyze the sign of \(f^{\prime}\)

From the relationship between the function \(f\) and its derivative \(f^{\prime}\), when \(x\in(-\infty, - 2)\cup(2,\infty)\), \(f^{\prime}(x)>0\), so \(f\) is increasing on \((-\infty,-2)\cup(2,\infty)\). When \(x\in(-2,2)\), \(f^{\prime}(x)<0\), so \(f\) is decreasing on \((-2,2)\).

Answer:

\(f\) is increasing on \((-\infty,-2)\cup(2,\infty)\); \(f\) is decreasing on \((-2,2)\)