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Core 1 OCR-Differentiation

nerdygeek123

Find the equation of the tangent to the curve y=x^2 which is parallel to the line y=x.

Reply 1

Jpw1097

Original post by nerdygeek123

Find the equation of the tangent to the curve y=x^2 which is parallel to the line y=x.

Firstly, you know that the gradient of the tangent is going to be 1, since it is parallel to the line y=x. Therefore, dy/dx=1

y=x^2 ==> dy/dx=2x. This is the equation of the gradient.

Since we know that the gradient is 1, we can equate this to the equation of the gradient to find the x and y points.

Using the x and y points and the gradient, we can find the equation of the tangent by plugging these values into y-y1=m(x-x1)

(edited 8 years ago)

Reply 2

Indeterminate

Original post by Jpw1097

Firstly, you know that the gradient of the tangent is going to be 1, since it is parallel to the line y=x. Therefore, dy/dx=1

y=x^2 ==> dy/dx=2x. This is the equation of the gradient.

Since we know that the gradient is 1, dy/dx also equals 1, therefore, 2x=1.
This means that x=1/2.

When x=1/2 ==> y=(1/2)^2 ==> y=1/4.

Therefore, the line that is parallel to y=x is tangent to the curve at the point (1/2, 1/4).

Using the equation y-y1=m(x-x1) we can work out the equation of the tangent, since x1=1/2, y1=1/4 and m=1.

y-1/4=1(x-1/2) ==> y-1/4=x-1/2 ==> y=x-1/4 ==> 4y=4x-1

But we're not meant to post full solutions :smile:

Reply 3

nerdygeek123

Original post by Jpw1097

Firstly, you know that the gradient of the tangent is going to be 1, since it is parallel to the line y=x. Therefore, dy/dx=1

y=x^2 ==> dy/dx=2x. This is the equation of the gradient.

Since we know that the gradient is 1, dy/dx also equals 1, therefore, 2x=1.
This means that x=1/2.

When x=1/2 ==> y=(1/2)^2 ==> y=1/4.

Therefore, the line that is parallel to y=x is tangent to the curve at the point (1/2, 1/4).

Using the equation y-y1=m(x-x1) we can work out the equation of the tangent, since x1=1/2, y1=1/4 and m=1.

y-1/4=1(x-1/2) ==> y-1/4=x-1/2 ==> y=x-1/4 ==> 4y=4x-1

Thank you this was really helpful!