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)

The explanation for the correct answer.
Solve for the range where the function $y=-x^2+6x-3$ is increasing.
$y=-x^2+6x-3$
Differentiating with respect to $x$, we get
$\begin{array}{l}y\prime =-2x+6\\ y\text{ is increasing if }y\prime >0\\ \Rightarrow -2x+6>0\\ \Rightarrow -2x>-6\\ \Rightarrow 2x<6\\ \Rightarrow x<3\end{array}$