The point on the curve y=12x−x2 where the tangent is parallel to x-axis, is

A
$(0, 0)$
B
$(2, 16)$
C
$(3, 9)$
D
(6, 36)

Solution:

Let $(x_{1}, y_{1})$ be the required point on $y = 12 x - x^{2}$

Then,

$\begin{array}{l} {(\frac{d y}{d x})}_{(x_{1}, y_{1})} = 0 \\ \Rightarrow 12 - 2 x_{1} = 0 \Rightarrow x_{1} = 6 [∵ y = 12 x - x^{2} \Rightarrow \frac{d y}{d x} = 12 - 2 x] \end{array}$

Since $(x_{1}, y_{1})$ lies on $y = 12 x - x^{2}$

$∴ y_{1} = 12 x_{1} - {x_{1}}^{2} \Rightarrow y_{1} = 72 - 36 = 36$

Hence, $(6, 36)$ is the required point

The point on the curve $y = 12 x - x^{2}$ where the tangent is parallel to x-axis, is

Solution:

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