Thread: can some one please help me finding the tangent and the norm please

i can find the tangent and the norm with some easy when the equation to start is something like
3x^2+8x+4 when x=1
but i have a new equation
3x^2+2xy^2+6=2y^3 and have to find the tangent and norm at point (2,3)
i can differentiate to get
6x+2x2y+2y^2=6y^2
but dont get how i use y=mx+c
if x=2 and y=3 this means
3=m2+c
all i get 4 m is 54 and i dont think this is right can u please put me on the right line thank you

Originally Posted by alpharebel10

i can find the tangent and the norm with some easy when the equation to start is something like
3x^2+8x+4 when x=1
but i have a new equation
3x^2+2xy^2+6=2y^3 and have to find the tangent and norm at point (2,3)
i can differentiate to get
6x+2x2y+2y^2=6y^2
but dont get how i use y=mx+c
if x=2 and y=3 this means
3=m2+c
all i get 4 m is 54 and i dont think this is right can u please put me on the right line thank you

You need to be careful when differentiating implicitly. For your function



you have which solving for y' gives

and at (2,3) this becomes , which is the slope of the tangent. Now the equation of the tangent is or . For the normal, use

Originally Posted by alpharebel10

i can find the tangent and the norm with some easy when the equation to start is something like

That's "normal", not "norm", which has quite a different meaning in mathmathics. Also it is not clear whether you want the tangent and normal lines or vectors. I will asume you mean lines.

3x^2+8x+4 when x=1
but i have a new equation
3x^2+2xy^2+6=2y^3 and have to find the tangent and norm at point (2,3)
i can differentiate to get
6x+2x2y+2y^2=6y^2

No, you don't. Since y is a function of x and you are differentiating with respect to x, you have to use the "chain rule". The derivative of 2xy^3, with respect to x, is, by the product rule 2y^2+ 2x(y^2)'= 2y^2+ 4xyy' and the derivative of 2y^3, with respect to x is 6y y'.
The derivative of 3x^2+ 2xy^2+ 6= 2y^3 is 6x+ 2y^2+ 4xyy'= 6y^2y'. Solve that for y' (when x= 2 and y= 3) and use that for your m.

but dont get how i use y=mx+c
if x=2 and y=3 this means
3=m2+c
all i get 4 m is 54 and i dont think this is right can u please put me on the right line thank you