Question

Determine Interval of Interval 1 or 2 is Positive or Negative

In calculus, how do you determine on which intervals a function is positive or negative based on its derivatives?

A) Analyze Critical Points
B) Evaluate Integral
C) Find Asymptotes
D) Compute Domain

Answer 1

In calculus, to determine on which intervals a function is positive or negative based on its derivatives, you can analyze critical points, create a number line, and test each interval using the derivative.

Step-by-step explanation:

In calculus, to determine on which intervals a function is positive or negative based on its derivatives, you can follow these steps:

1. Analyze critical points: Set the derivative equal to zero and solve for x to find the critical points.
2. Create a number line: Mark the critical points on a number line.
3. Test each interval: Choose a test value from each interval and plug it into the derivative. If the derivative is positive, the function is increasing on that interval, so it is positive. If the derivative is negative, the function is decreasing on that interval, so it is negative.

By following these steps, you can determine the intervals on which a function is positive or negative based on its derivatives.