Question

Consider the following statements in respect of the function $f(x)=x^{3}-1, x \in[-1,1]$ 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

Answer 1

Answer: (A)

Only I

Answer 2

Since $f (x)$ is an increasing function in $[- 1, 1]$ and it has a root in $(- 1, 1)$.
$\therefore$ Only statement I is correct.