Question

Consider the following statements in respect of the function f(x)=x³-1, x∈[-1,1]. I. f(x) is increasing in [-1,1] II. f(x) has no root in (-1,1). Which of the statements given above is/are correct?

• A. Only I
• B. Only II
• C. Both I and II
• D. Neither I nor II

Hint:

A function with f'(x)\ge0 on an interval is increasing on that interval.

Answer 1

The Correct Option is A

Step 1: f'(x)=3x²\ge0 for all x. Hence, f(x) is increasing on [-1,1].
Step 2: Root of f(x)=0 is x=1, which is not in (-1,1). Thus, only statement I is correct.