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If $f : [2, 3] \to R$ is defined by $f (x) = x^{3} + 3 x - 2,$ then the range $f (x)$ is contained in the interval:

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$[35, 50]$

$[12, 34]$

$[1, 12]$

$[- 12, 12]$

answer is B.

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Detailed Solution

$f (x) = x^{3} + 3 x - 2 \Rightarrow f' (x) = 3 x^{2} + 3 > 0, \forall x \in R \Rightarrow f i s s t r i c t l y i n c r e a \sin g ∴ r a n g e o f f = [f (2), f (3)] = [12, 34]$

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