Let f ( x ) = 4 x 3 - 11 x 2 + 8 x - 5 , x R . Then f :

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Solution

Q.
Let $f (x) = 4 x^{3} - 11 x^{2} + 8 x - 5, x \in R$ . Then $f$ :

1 has a local minima at $x = \frac{1}{2}$

2 has a local minima at $x = \frac{3}{4}$

3 is increasing in $(\frac{1}{2}, \frac{3}{4})$

4 is decreasing in $(\frac{1}{2}, \frac{4}{3})$

Ans.
(4)

$Let f (x) = 4 x^{3} - 11 x^{2} + 8 x - 5, \forall x \in R$

$\Rightarrow f' (x) = 12 x^{2} - 22 x + 8 and f' (x) > 0$

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