need c3 help

[T.Q]

A curve C has equation

y=3sin2x+4cos2x,

The point A(0, 4) lies on C.
 
(a) Find an equation of the normal to the curve C at A

when i defferintiate i got this dy/dx= 6cos2x - 8sin2x

my problem was when i subsituted the  x=0 i had the wrong value of the gradient

in the MS m=6

show your working

[astarmathsandphysics]

A curve C has equation

y=3sin2x+4cos2x,

The point A(0, 4) lies on C.
 
(a) Find an equation of the normal to the curve C at A


show your working

dy/dx=6cos2x-8sin2x so gradient m=6cos(2*0)-8sin(2*0)=6 and m for normal is -1/6
y-y1=m(x-x1)
y-4=-1/6(x-0) so y=-x/6+4

[T.Q]

dy/dx=6cos2x-8sin2x so gradient m=6cos(2*0)-8sin(2*0)=6 and m for normal is -1/6
y-y1=m(x-x1)
y-4=-1/6(x-0) so y=-x/6+4

thanx now i got it