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Problem 63

Prove that the function $f(x)=x^{101}+x^{51}+x+1$…


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Problem 62

Show that 5 is a critical number of the function
$g(x)=2+(x-5)^{3}$ but $g$ does not have a local extreme
value at $5 .$


$x=5$ is a critical number because $g^{\prime}(5)=3(5-5)^{2}=0$


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