Question

The point on the curve $y=x^2+7x+2$ closest to the line $y=3x-3$ is $\cdots \cdots$

• A. $(-2,-8)$
• B. $(-8,-2)$
• C. $(2,8)$
• D. $(8,2)$

Answer 1

The correct option is A $(-2,-8)$

Let P(x,y) be a point on the curve
$y=x^2+7x+2$
$3x-3=x^2+7x+2$
$f\left(x\right)=x^2+4x+5$
$f^{\prime }\left(x\right)=2x+4$
For maxima or minima,
$f^{\prime }\left(x\right)=0$
$\Rightarrow x=-2$
$f^{\prime \prime }\left(x\right)=2>0$
Hence,f(x) has a minimum at $x=-2$
$\Rightarrow y=-8$
Hence, the point is (-2,-8).