NIMCET 2012 Question Paper with solutions

Given curve,
y = 6x - ${\mathit{x}}^2$ ... (i)
On differentiating w.r.t x,
$\frac{\mathit{d}\mathit{y}}{\mathit{d}\mathit{x}}$ = 6 - 2x
Since , Slope of tangent parallel to x-axis is $\frac{\mathit{d}\mathit{y}}{\mathit{d}\mathit{x}}$ = 0
∴ 6 - 2x = 0 ⇒ x = 3 [from Eq. (i)]
y = 6 (3) - ${\left(3\right)}^2$ = 18 - 9
y = 9
∴ Only one point (3, 9) at which the tangent is parallel to x-axis.