Thread: the equation of normal problem

1. the equation of normal problem

this is the question:the normal to the curve y=X^3-2X^2 at the point (1,-1)passes through the point(p,2p).calculate the value of p.

2. Originally Posted by mastermin346
this is the question:the normal to the curve y=X^3-2X^2 at the point (1,-1)passes through the point(p,2p).calculate the value of p.

HI

$y=x^3-2x^2$

$\frac{dy}{dx}=3x^2-4x$ and this is the gradient of tangent

$=3(1)-4$

$=-1$

Then using this formula , $y-y_1=m(x-x_1)$

you will find that the equation of normal is y=x-2

so this equation passes through (p,2p)

$2p=p-2$

$
p=-2
$