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# The point on the curve

Question:

The point on the curve $y=12 x-x^{2}$ where the slope of the tangent is zero will be

A. $(0,0)$

B. $(2,16)$

C. $(3,9)$

D. $(6,36)$

Solution:

Given that the curve $y=12 x-x^{2}$

The slope of the curve $\frac{d y}{d x}=12-2 x$

Given that the slope of the tangent $=0$

$\Rightarrow 12-2 x=0$

$\Rightarrow x=6$

So, $y=72-36$

$\Rightarrow y=36$

So, the correct option is $D$.