Given the equation y=xβ11β,
m=dxdyβ=β(xβ1)21β=β1(given)
βΉ(xβ1)21β=11=(xβ1)21=x2β2x+11β1=x2β2x0=x(xβ2)βΉx=0 and x=2 For x=0,
y=0β11β=β11β=β1β΄the tangent line touches the curve at the point (0,-1)
The equation of the line is:
yβy1β=m(xβx1β)yβ(β1)=β1(xβ0)y+1=βxβΉx+y=β1β―(i) at x=2,
y=2β11β=11β=1β΄the tangent line touches the curve at the point (2,1)
yβy1β=m(xβx1β)yβ(β1)=β1(xβ2)yβ1=βx+2βΉx+y=3β―(ii) Thus, eqn (i) and (ii) are the required equations of the line that are tangential to the curve.
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