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2 Answers

Best answer
16 votes
16 votes

$$P(x) = x^2 - 2x +5$$

Since a polynomial is defined and continuous everywhere, we only need to check the critical point and the boundaries.

$\dfrac{d}{dx}P(x) = 2x - 2$

Critical point: $2x-2 = 0\implies x = 1$ gives $P(x) = 4$, which is the minimum.

Boundaries: $\lim_{x \to \color{red}{0}^+} P(x) = \lim_{x \to \color{red}{2}^-} P(x) = 5$

Since $P(x)$ increases as $x$ goes farther away from the $1.$ But $P(x)$ being defined on an open interval, it never attains a maximum!

Hence, e. None of the above is the correct answer.

3 votes
3 votes

We could have check boundary conditions but given is an open interval.

Answer:

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