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Numerade Educator

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Problem 92 Medium Difficulty

For what values of $ c $ is the function
$$ f(X0 = cx + \frac{1}{x^2 + 3} $$
increasing on $ (-\infty, \infty) $?

Answer

For all $c>\frac{1}{8} \quad f(x)$ is increasing on $(-\infty,+\infty)$

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Video Transcript

Okay, So rest. For what? About gypsies that function after effects. Because here, because one of the exquisite street is increasing from negative infinity infinity. So first, we're gonna take the first derivative. So when you think the derivative we get so you might have to act over X square plus three squared and we have to set this equal to greater than zero, and then you can bring the sea over. So when you do that you get to see is greater than two acts over expert Plus three, and that's squared. And so where does this occur? Or yes, Leo, it's just if you grafted. And so you're looking for where there is some sort of wars on attention, she and when you go out the function, the words on attention that's that one comma zero point one two five. So that means the value of sea has to be greater than your point one two five for this to be true, and that's it.