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Find the tangent to the curve y=x^2 at point (1,2) by differentiation method.
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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.`
Posted by sciencesolve on May 10, 2013 at 12:28 PM (Answer #1)
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