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Specialist exam 1 2007 Q 3

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

Got stuck on


--- Quote ---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).
--- End quote ---

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 :D

midas_touch:

--- Quote from: Mao on March 09, 2008, 02:18:30 pm ---



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 :D

--- End quote ---

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]

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