Find the equations of the tangent and normal to the curve y=x^3-2x^2-2x-3 at x=2?
1 Answer
Sep 1, 2017
Tangent:
Normal:
Explanation:
A tangent line would have a gradient equal to that of the curve at x=2, while a normal line would have a gradient which is the negative reciprocal of that of the curve at x=2
When x=2,
Hence, tangent at x=2:
Solve for c by setting
Thus,
The equation of the tangent line is thus
graph{(y-x^3+2x^2+2x+3)(y-2x+11)=0 [1, 3, -7.5, -6.5]}
Similarly, for the normal line,
Thus the equation of the normal line is
graph{(y-x^3+2x^2+2x+3)(y+1/2x+6)=0 [1, 3, -7.5, -6.5]}