Question

From the graph below, what are the two intervals that the function is increasing on?

Answer 1

(-∞, -1) and (2, ∞)

Explanation:

A function is increasing when the slope is positive (y gets bigger as x gets bigger)

A function is decreasing when the slope is negative (y gets smaller as x gets bigger)

At the turning points (stationary points) the slope is zero.

Therefore, from inspection of the graph:

• increasing → (-∞, -1)
• decreasing → (-1, 2)
• increasing → (2, ∞)

Answer 2

Explanation:

The graphed function has its local maximum at x = - 1 and local minimum at x = 2.

The function is decreasing between those points and increasing outside.

The increasing intervals are

• x ∈ (- ∞, - 1) ∪ (2, + ∞)