Question

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

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

Answer 1

Answer: (B)

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

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