SOLUTION: Find the equations of the tangents to the curve y = x^3 - x^2 - 2 at the point where x = 2. Find the coordinates of the point where the tangent intersect the curve.

Algebra ->  Coordinate-system -> SOLUTION: Find the equations of the tangents to the curve y = x^3 - x^2 - 2 at the point where x = 2. Find the coordinates of the point where the tangent intersect the curve.      Log On


   

Question 1121468: Find the equations of the tangents to the curve y = x^3 - x^2 - 2 at the point where x = 2. Find the coordinates of the point where the tangent intersect the curve.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
dy%2Fdx=3x%5E2-2x
-
atx=2,
dy%2Fdx=3%2A2%5E2-2%2A2=4%283-1%29=8


Point of tangent meeting the curve,
y=2%5E3-2%5E2-2=3
... (2,3)

Equation for the tangent line to the curve:
highlight%28y-3=8%28x-2%29%29


Maybe you can answer the second question.
(Hint: y=y)