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Find the equation of the tangent to the ...

Find the equation of the tangent to the curve `y=3x^(2)-x+1` at P(1, 3).

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`y=3x^(2)-x+1`
Differentiating w.r.t. x, we get,
`(dy)/(dx)=(d)/(dx)(3x^(2)-x+1)=3xx2x-1+0=6x-1`
`:. ((dy)/(dx))_("at" P(1, 3))=6(1)-1=5`
= slope of the tangent at P(1, 3)
`:.` the equation of the tangent at P is `y-3=5(x-1)`
`:.y-3=54x-5" ":.5x-y-2=0`.
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