| Directions: (11 - 15) |
| The shape of a toy is given as \[f(x)=6(2{{x}^{4}}-{{x}^{2}}).\]To make the toy beautiful 2 sticks which are perpendicular to each other were placed at a point (2, 3), above the toy. |
A) \[\pm \frac{1}{4}\]
B) \[\pm \frac{1}{2}\]
C) ±1
D) None
Correct Answer: B
Solution :
\[f(x)=6\left( 2{{x}^{4}}-{{x}^{2}} \right)\] \[\Rightarrow f'\left( x \right)=6\left( 8{{x}^{3}}-2x \right)=12\left( 4{{x}^{3}}-x \right)\] For critical points, \[f'\left( x \right)=0\Rightarrow 12x(4{{x}^{2}}-1)=0\] \[\Rightarrow x=0,\,\,x=\pm \frac{1}{2}\] \[\left[ \because \,\,x\ne 0 \right]\]
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