Question

A function \(f(x) = \frac{x^2 - 3x + 2}{x^2 + 2x - 3}\) is

• A. maximum at \(x = -3\)
• B. maximum at \(x = -3\) and maximum at \(x = 1\)
• C. maximum at \(x = 1\)
• D. function is increasing in its domain

Hint:

Cancel common factors after factoring.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Find derivative and check sign.
Step 2: Detailed Explanation:
\(f(x) = \frac{(x-1)(x-2)}{(x+3)(x-1)} = \frac{x-2}{x+3}\) for \(x \neq 1, -3\)
\(f'(x) = \frac{(x+3) - (x-2)}{(x+3)^2} = \frac{5}{(x+3)^2}>0\)
So function is increasing in its domain (except at \(x = 1, -3\) where undefined).
Step 3: Final Answer:
Increasing in its domain.