Class 12

Math

Calculus

Application of Derivatives

Find the equation of all lines having slope $1$that are tangents to the curve $y=x−11 ,x=1$.

$y=x−11 $

$∴$ Slope of tangent,$(dxdy )=−(x−1)_{2}1 $

Slope of tangent to this curve is given $−1$.

$∴−(x−1)_{2}1 =−1$

$∴x=0andx=2$

$⇒y=−1andy=1$

Therefore, equation of tangents to the given curve,

$x−0y+1 =−1andx−2y−1 =−1$

$⇒x+y+1=0andx+y−3=0$, which are the required equations.