EASY ALGEBRA

The derivative of the given $p(x) = 3x^{2} - 5x +2$ with respect to $x$ is $6x - 5$ , 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 $6x-5=0 \Rightarrow x = \dfrac{5}{6}$ . Hence, the minimum value is $p(\dfrac{5}{6}) = \boxed{-0.083}$ .

Differentiate polynomial wrt x,

$6x-5=0\Rightarrow x=\frac{5}{6}$

Substitute x to calculate minima which comes out to be $\frac{-1}{12}=-0.082$

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