What is the x coordinate of the point on the curve f(x)=`sqrt(x)(7x-6)` where the tangent is parallel to x axis ?

Options

A. `-(1)/(3_`
B. `2/7`
C. `6/7`
D. `1/2`

Answer

B

Explanation

`f(x)=sqrt(x)(7x-6)=7x^(3//2)-6x^(1//2)`
`f(x)=7xx3/2x^(1//2)-6xx1/2x^(-1//2)`
when tangent is parallel to x axis f(x) =0
or `21/2 x^(1//2) -3x^(-1//2)=0`
`21/2 sqrt(x)=(3)/sqrt(x)`
or `7x=2 rarr x= 2/7`