Question

question 1
the function graphed above has:
positive derivative on the interval(s)
negative derivative on the interval(s)
question help: video

Explanation:

Step1: Understand derivative sign from graph

A positive derivative means the function is increasing (graph rises as \( x \) increases), a negative derivative means the function is decreasing (graph falls as \( x \) increases).

Step2: Analyze increasing intervals

From the graph, the function increases from \( x = -2 \) to \( x = 2 \) (since it rises from the minimum at \( x=-2 \) to the maximum at \( x = 2 \)). So the interval with positive derivative is \( (-2, 2) \).

Step3: Analyze decreasing intervals

The function decreases when \( x < -2 \) (from left to \( x=-2 \)) and when \( x > 2 \) (from \( x = 2 \) to the right). So the intervals with negative derivative are \( (-\infty, -2) \) and \( (2, \infty) \).

Answer:

Positive derivative on the interval(s): \(\boldsymbol{(-2, 2)}\)
Negative derivative on the interval(s): \(\boldsymbol{(-\infty, -2) \cup (2, \infty)}\)