Q101 / 180 · KCET 2007 · Mathematics

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

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

Solution

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

Hence, the correct answer is option: 'B'.

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