A) \[(2,-16),(-2,16)\]
B) (3, 10), (0, 10)
C) \[(2,16),(-2,-16)\]
D) None of these
Correct Answer: C
Solution :
Given, curve is \[y=12x-{{x}^{3}}\] Slope \[\frac{dy}{dx}=0\] \[\Rightarrow \]\[12-3{{x}^{2}}=0\] \[\Rightarrow \] \[3{{x}^{2}}=12\] \[\Rightarrow \] \[{{x}^{2}}=4\Rightarrow x=\pm 2\] At \[x=+2,\] \[y=24-{{(2)}^{3}}=24-8=16\] At \[x=-2,\] \[y=-24+8=-16\] Hence, required points are (2, 16),\[(-2,-16)\].
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