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

The correct option is A

$x<3$

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

$y\text{'}=–2x+6$

$y$ is increasing if $y\text{'}>0$

$$\begin{gathered} \Rightarrow –2x+6>0 \\ \Rightarrow –2x>-6 \\ \Rightarrow 2x<6 \\ \Rightarrow x<3 \end{gathered}$$

Hence, option (A) is the correct answer.