Download Find the equation of the tangent to the curve

Find the equation of the normal to the curve
y=(2x + 3)(x – 1) at the point where x=-1
Find full co-ordinate …. y = (-2+3)(-1-1) = -2 so (-1, -2)
Expand equation of curve y = (2x + 3)(x – 1) = 2x2 + x -3
Find gradient function of curve ….
dy
= (2)(1) = 2
dx
Find gradient function of curve…..
dy
= 4x + 1
dx
So gradient of tangent at x=-1…..
So gradient of normal =
dy
=2
dx
1
3
So gradient of tangent at x=-1 ……
dy
= 4 (-1) + 1 = -3
dx
So gradient of normal at x=-1 ……
dy
= 4 (-1) + 1 = -3
dx
So equation of normal to the curve at (-1, -2) is
1
(x + 1)
3
1
2
y= x-1
3
3
y+2=

So equation of normal to the curve at (-1,-2) is
y + 2 = -3 (x + 1)

y = -3x - 5
Solve
dy
= 2x – 6 = 0, so x = 3
dx