NIMCET 2012 — Mathematics PYQ

When a tangent is parallel to the $X$-axis, its slope is zero. In calculus, the slope of the tangent is given by the derivative $\frac{dy}{dx}$.

So, we must have:

2. Differentiating the Equation:

Given the curve:

Differentiating with respect to $x$:

3. Finding the $x$-coordinate:

Set the derivative to zero:

4. Finding the $y$-coordinate:

Substitute $x=3$ back into the original curve equation:

Conclusion:

The required point is $(3,9)$.

Correct Option:

(d) (3,9)