Question

Which statement is true regarding the intervals where the function is increasing and decreasing?

The function is increasing from (–∞, 0).
The function is increasing from (0, ∞).
The function is decreasing from (–∞, 0).
The function is decreasing from (–∞, ∞).

Answer 1

I can’t tell which choice is correct without the function or its graph. Please paste the function or an image of the graph.

How to decide (so you can check quickly):
1. Compute f′(x) (or read slope from the graph).
2. Find critical points where f′(x)=0 or undefined.
3. Test the sign of f′(x) on each interval determined by those points:
- f′>0 on an interval → f is increasing there.
- f′<0 on an interval → f is decreasing there.

Quick examples:
- f(x)=x^2: f′(x)=2x, so f is decreasing on (−∞,0) and increasing on (0,∞). (So the second and third choices would both be true for x^2.)
- f(x)=x^3: f′(x)=3x^2≥0, so f is increasing on (−∞,∞). (Fourth choice true.)
- f(x)=−x^2: f′(x)=−2x, so increasing on (−∞,0) and decreasing on (0,∞). (First choice true.)

Send the function/graph and I’ll pick the correct option.