On [ − 2 , 3 ] , let f ( 1 ) = − 6 and f ( x ) = ( x 3 − 2 x 2 − 5 x + 6 ) / ( x − 1 ) for x  = 1 . Which is true?

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MathematicsApplication of DerivativeMonotonicity-Rolle's-theroemMedium2 minQB

MathematicsMediumsingle choice

On $[- 2, 3]$ , let $f (1) = - 6$ and $f (x) = (x^{3} - 2 x^{2} - 5 x + 6) / (x - 1)$ for $x \neq = 1$ . Which is true?

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Answer:

Solution:

The numerator factors by $x - 1$ , and the continuation value is -6 , so $f$ is continuous and differentiable. Also $f (- 2) = f (3) = 0$ . Solving $f (c) = 0$ yields $c = 1/2$ .

Stream:JEESubject:MathematicsTopic:Application of DerivativeSubtopic:Monotonicity-Rolle's-theroem

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