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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).

A

`y=5x+2`

B

`y=5x-2`

C

`y=(1)/(5)x+2`

D

`y=(1)/(5)x-2`

Text Solution

Verified by Experts

The correct Answer is:
B
`y=3x^(2)-x+1`
`therefore" "(dy)/(dx)=6x-1`
`" "((dy)/(dx))_("(1, 3)")=6-1=5`
`therefore" "m=5`
Equation of tangent
`y=mx+c`
`y=5x+c" …(i)"`
Put (1, 3) in equaiton (i),
`3=5xx1+c`
`therefore" "c=-2`
Equation of tangent `y=5x-2`
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