Application of Derivatives
Tangents and Normals
IIT-JEE 1990
Grade 12
Question:
The $x$-coordinates of the points on the curve $y = x^3 - 3x^2 - 9x + 5$ where the tangent is parallel to the $x$-axis are:
(1) $1, 3$
(2) $-1, 3$
(3) $-1, -3$
(4) $0, 3$
Step-by-Step Solution
Key Concept: Set $dy/dx = 0$ and solve the resulting quadratic equation in $x$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)