The minimum value of f(x) = x4 - x2 - 2x + 6 is _____________ .

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4 	ext { Given:} f\left( x ight) = x^4 - x^2 - 2x + 6 \Rightarrow f'\left( x ight) = 4 x^3 - 2x - 2 \Rightarrow f'\left( x ight) = \left( x - 1 ight)\left( 4 x^2 + 4x + 2 ight) 	ext { For a local maxima or a local minima, we must have } f'\left( x ight) = 0 \Rightarrow \left( x - 1 ight)\left( 4 x^2 + 4x + 2 ight) = 0 \Rightarrow \left( x - 1 ight) = 0 \Rightarrow x = 1 	ext { Now,} f''\left( x ight) = 12 x^2 - 2 \Rightarrow f''\left( 1 ight) = 12 - 2 = 10 > 0 	ext { So, x = 1 is a local minima } . 	ext { The local minimum value is given by } f\left( 1 ight) = 1 - 1 - 2 + 6 = 4

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