Consider the following statements in respect of the function f ( x ) = x 3 − 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?

Mathematics - Application of Derivative Question with Solution | TestHub

MathematicsApplication of DerivativeMonotonicity-Increasing-DecreasingEasy2 minPYQ_2016

MathematicsEasysingle choice

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?

Options:

Answer:

Solution:

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

Stream:BITSATSubject:MathematicsTopic:Application of DerivativeSubtopic:Monotonicity-Increasing-Decreasing

⏱ 2mℹ️ Source: PYQ_2016

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