Question

Let $f(x)=\begin{cases}-x^2 & , x<0 \\ x^2+8, & x \geq 0\end{cases}$ Equation of tangent line touching both branches of $y=f(x)$ is

• A. $y=4 x+1$
• B. $y=4 x+4$
• C. $y=x+4$
• D. $y=x+1$

Answer 1

Answer: (B)

Let $y=m x+c$ be tangent touching both branches.
$f(x)=-x^2, y=m x+c$
$ x < 0 $

$x ^2+ mx + c =0, m >0 (\because x <0)$ (negative roots)
$D=0 \Rightarrow m^2=4 c$
$f(x)=x^2+8, y=m x+c, x>0$
$x^2-m x+8-c=0, m>0$(positive roots)
$D=0 \Rightarrow m^2=32-4 c$
$\Rightarrow c=4, m^2=16 \Rightarrow c=4, m=4$