# Find the equations of the tangent and normal to the given curves at the indicated points: $(iii) \: y = x^3\; at \;(1, 1)$

This is third part of the multi-part question q14

## 1 Answer

Toolbox:
• Equation of the tangent at $(x_1,y_1)$ where slope is $m$ is given by $y-y_1=m(x-x_1)$
• Equation of the normal at $(x_1,y_1)$ where slope is $m$ is given by $y-y_1=\large\frac{-1}{m}$$(x-x_1) Step 1: Given : y=x^3 Differentiating w.r.t x we get, \large\frac{dy}{dx}_{(1,1)}$$=3(1)$
$m=3$
Step 2:
Therefore equation of the tangent at $(1,1)$ is $(y-1)=3(x-1)$
$\Rightarrow 3x-y-2=0$
Step 3:
Equation of the normal at $(1,1)$ is $(y-1)=\large\frac{-1}{3}$$(x-1)$
$\Rightarrow 3y-3=-x+1$
$\Rightarrow x+3y-4=0$
answered Jul 11, 2013

1 answer

1 answer

1 answer

1 answer

1 answer

1 answer

1 answer