The minimum value of the polynomial p ( x ) = 3 x 2 − 5 x + 2
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Differentiate polynomial wrt x,
6 x − 5 = 0 ⇒ x = 6 5
Substitute x to calculate minima which comes out to be 1 2 − 1 = − 0 . 0 8 2
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The derivative of the given p ( x ) = 3 x 2 − 5 x + 2 with respect to x is 6 x − 5 , and we know that an extrema is attained when the slope of the tangent drawn to the graph at that point is 0 . Hence, equating slope as a function of x to be 0 , we get 6 x − 5 = 0 ⇒ x = 6 5 . Hence, the minimum value is p ( 6 5 ) = − 0 . 0 8 3 .