Question

If the curves $y=x^3-3x^2-8x-4$ and $y=3x^2+7x+4$ touch each other at a point P then the equation of common tangent at P is?

• A. $x-y+1=0$
• B. $2x-y+1=0$
• C. $x+y+1=0$
• D. $2x+y+1=0$

Answer 1

The correct option is A $x-y+1=0$

$3x^2+7x+4=x^3-3x^2-8x-4$

$x^3-6x^2-15x-8=0$

$(x+1{)}^2(x-8)=0$

Putting x = -1 in the above equation, we get

$y=3-7+4$

$y=0$

and putting x = 8 in the above equation,we get

$y=3x^2+7x+4$

$y=252$

The points are $(8,252)$ and $(-1,0)$

Equation of the tangent -

$\frac{dy}{dx}=6x+7$

$\frac{dy}{dx}=1$ or $55$

$y=mx+c$

$y=x+c$ or $y=55x+c$

$c=1$ or $c=188$

Equation = $y=x+1$ or $y=55x+188$