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Find the tangent to the curve y=x^2 at point (1,2) by differentiation method.

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mehta1996 | Student, Grade 10 | eNotes Newbie

Posted May 10, 2013 at 12:07 PM via iOS

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Find the tangent to the curve y=x^2 at point (1,2) by differentiation method.

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted May 10, 2013 at 12:28 PM (Answer #1)

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You need to write the equation of tangent line to the curve, at the point `(1,2), `  such that:

`y - 2 = (dy)/(dx)|_(x=1)(x - 1)`

You need to differentiate the given function `y = x^2` with respect to x, such that:

`(dy)/(dx) = 2x`

Evaluating `(dy)/(dx)` at `x = 1` yields:

`(dy)/(dx)|_(x=1) = 2`

Replacing 2 for `(dy)/(dx)|_(x=1)` yields:

`y - 2 = 2(x - 1) => 2x - y - 2 + 2 = 0 => y = 2x`

Hence, evaluating the equation of tangent line to the given curve, at `(1,2)` , using differentiation method, yields `y = 2x.`

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oldnick | Valedictorian

Posted May 11, 2013 at 12:17 AM (Answer #2)

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`y=x^2`    `y'=2x`      `y'(1)=2`

So:

 

`y-2=2(x-1)`     `y=2x`

Notethe point `P(1;2) `  doesn't lay on parabolas

 

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