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Monotonically Increasing Functions

If x= α and x...

Question

If $x = α$ and $x = β$ are the points of inflection $(α < β)$ of the curve $y = 3 x^{4} - 4 x^{3},$ then the value of $2 α + 3 β$ is

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Solution

Given, $y = 3 x^{4} - 4 x^{3}$
$\Rightarrow y^{'} = 12 x^{3} - 12 x^{2}$
$\Rightarrow y^{''} = 36 x^{2} - 24 x$
For P.O.I. $y^{''} = 0$
$\Rightarrow 36 x^{2} - 24 x = 0$
$\Rightarrow 12 x (3 x - 2) = 0$
$\Rightarrow x = 0$ and $x = \frac{2}{3}$
So, $α = 0$ and $β = \frac{2}{3}$
$\Rightarrow 2 α + 3 β = 2$

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Monotonically Increasing Functions

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