Using Lagranges mean value theorem, find a point on the curve `y=sqrt(x-2)` defined on the interval [2,3], where the tangent is parallel to the chord joining the end points of the curve.

Options

A. x= `9/2`
B. x= `9/4`
C. x= `3/2`
D. None of these

Answer

C

Explanation

`y^2=x-2`

`y=sqrt(x-2`

taangent at(a,b)

`dy/dx=1/(2sqrt(x-2`

`dy/dx=1/(2sqrt(a-2`

Slope of chord`=(1-0)/(3-2)=1`

`1/(2sqrt(a-2))=1`

`1/sqrt(a-2)=2`

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