Specialist exam 1 2007 Q 3

[Captain]

Got bored so looking at some of the questions from last year.

Got stuck on

Find the equation of the tangent to the curve x^3−2(x^2)y+2(y^2)=2 at the point P(2, 3).

Working out would be appreciated, thanks

[unknown id]

u hav to use implicit differentiation to find the derivative

[Mao]

When we implicitly differentiate u (an expression in terms of y), we'll have:


so



using the product rule on the middle term:








with that, you can sub in P(2,3) and find you tangent

[midas_touch]

When we implicitly differentiate u (an expression in terms of y), we'll have:


so



using the product rule on the middle term:








with that, you can sub in P(2,3) and find you tangent

That only gives you the gradient of the tangent. Once you have this, you can find the equation by simply subbing in the x and y values into y = mx + c, where m is the gradient you just found.

[AppleXY]

or you could use the point-slope method.

y-y1 = dy/dx|(2,3)*[x-x1]