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# Core 3 - Differentiation

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1. the tangent to the curve y =3x (1+2x)^1/2 at the point (4,36) meets the x-axis at P and y -axis at Q =. Prove that the area of the triangle OPQ, where O is the origin, is 128/3 units squared

do you use the fact that y' = v'u +u"v??

so y'= 3(1 + 2x)^-1/2 (x + (1+ 2x)^-1)

then plug x=4 to find the gradient
then make the equation of the line : y= 5x -16
then find x and y
then 1/2(x)(y)
I get 128/5 units squared so i dont know what ive done wrong???
2. (Original post by Custardcream000)
the tangent to the curve y =3x (1+2x)^1/2 at the point (4,36) meets the x-axis at P and y -axis at Q =. Prove that the area of the triangle OPQ, where O is the origin, is 128/3 units squared

do you use the fact that y' = v'u +u"v??

so y"= 3(1 + 2x)^-1/2 (x + (1+ 2x)^-1)

then plug x=4 to find the gradient
then make the equation of the line : y= 5x -16
then find x and y
then 1/2(x)(y)
I get 128/5 units squared so i dont know what ive done wrong???
y'' implies the second derivative, you don't need that.

3. (Original post by RDKGames)
y'' implies the second derivative, you don't need that.

is y' = v'u +u'v the correct method?
4. (Original post by Custardcream000)
is y' = v'u +u'v the correct method?
Yes.
5. (Original post by RDKGames)
Yes.

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