Discussion
Let \(y = 3x^{2} - 6x + 10\). Which value of \(y\) minimizes this function ?
Answer: A
The function is minimized at 1, the value of \(x\) (the paper writes 'value of \(y\)', but the options are values of the variable \(x\)).
\[ \begin{aligned} \frac{dy}{dx} &= 6x - 6 = 0 \Rightarrow x = 1 \\ \frac{d^{2}y}{dx^{2}} &= 6 \gt 0 \end{aligned} \]
The positive second derivative confirms a minimum. The minimum value of the function itself is \(y = 3 - 6 + 10 = 7\), which is not among the options, so the question can only be asking for \(x\).
At \(x = 0\), 2 and 3 the function takes the values 10, 10 and 19, all larger than 7.
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