Question

The function f(x) = x² - 2x is strictly decreasing in the interval

• A. (-∞, 1)
• B. (1, ∞)
• C. R
• D. (-∞, ∞)

Answer 1

The Correct Option is A

We are given the function \( f(x) = x^2 - 2x \).
Step 1: Find the derivative of \( f(x) \)}
The derivative of the function is: \[ f'(x) = \frac{d}{dx} (x^2 - 2x) = 2x - 2 \]
Step 2: Find where \( f'(x) < 0 \)}
For the function to be strictly decreasing, we need: \[ f'(x) < 0 \] This gives: \[ 2x - 2 < 0 \] Solving for \( x \): \[ 2x < 2 \] \[ x < 1 \] Thus, the function is strictly decreasing in the interval \( (-\infty, 1) \).

Therefore, the correct answer is (A) \( (-\infty, 1) \).