Question

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

• A. $x<3$
• B. $x>3$
• C. $7<x<8$
• D. $5<x<6$

Answer 1

Answer: (A)

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