\(y=7 x^3+11 ; \)
\(\frac{d y}{d x}=21 x^2\)
at \(x=2, y=67\)
Slope of tangent \(=21.4=84\)
Eqn. of tangent at (2, 67) is \(y-y_1=\) slope \(\left(x-x_1\right)\)
\(\Rightarrow y-67=84(x-2)\)
\(\Rightarrow y-67=84 x-168\)
\( \Rightarrow 84 x-y=101\) ....(i)
at \(x=-2, y=-56+11=-45\)
Slope of tangent = 84 eqn of tangent is \(y-y_1=\) slope \(\left(x-x_1\right)\)
\(\Rightarrow y-(-45)=84(x+2) \)
\(\Rightarrow y+45=84 x+168 \)
\(\Rightarrow 84 x-y=-123\) ....(ii)
Eqn. (i) and (ii) are parallel.
