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$ f(x)$ is a differentiable function and selected values are given in the table above. Which of the following statements could be false?

$ f(x)=0$ at some point on the interval $[1,5]$.

$ f^\prime(x)=0$ at some point on the interval $(1,5)$.

$f(4)$ is a relative minimum.

$f(x)=7$ at some point on the interval $[1,5]$

$f^\prime(x)=-7$ at some point on the interval $(1,5)$.