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  4. The range in which y=-x2+6x-3 is increasing, is

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Q. The range in which $ y=-x^{2}+6x-3$ is increasing, is

ManipalManipal 2008

Solution:

Given, $y=-x^{2}+6 x-3$
$\Rightarrow \frac{d y}{d x}=-2 x+6=y'$
$y$ is increasing, if $y' > 0$
$\Rightarrow -2 x+6 > 0$
$\Rightarrow -2 x > - 6$
$\Rightarrow 2 x < 6$
$\Rightarrow x < 3$