turkey-yks 2021 Q10

turkey-yks · Other · yks-ayt Stationary points and optimisation Existence or properties of extrema via abstract/theoretical argument

A polynomial $P(x)$ with real coefficients and of degree four satisfies the inequality
$$P(x) \geq x$$
for every real number $x$.
$$\begin{aligned} & P(1) = 1 \\ & P(2) = 4 \\ & P(3) = 3 \end{aligned}$$
according to, $\mathbf{P(4)}$ is equal to what?

A polynomial $P(x)$ with real coefficients and of degree four satisfies the inequality

$$P(x) \geq x$$

for every real number $x$.

$$\begin{aligned}
& P(1) = 1 \\
& P(2) = 4 \\
& P(3) = 3
\end{aligned}$$

according to, $\mathbf{P(4)}$ is equal to what?

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