For what values of c is the function increasing on negative infinity to infinity?

Deinosuchus383

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Q. For what values of c is the function \(\displaystyle \, f(x)\, =\, cx\, +\, \dfrac{1}{x^2\, +\, 3}\,\) increasing on \(\displaystyle \, \left(-\infty,\, \infty\right)?\)

I know that in general you have to find out where the the slope is positive/negative to know where it is increasing or decreasing but I don't really know where to start with problems with constants.
 
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Q. For what values of c is the function \(\displaystyle \, f(x)\, =\, cx\, +\, \dfrac{1}{x^2\, +\, 3}\,\) increasing on \(\displaystyle \, \left(-\infty,\, \infty\right)?\)

I know that in general you have to find out where the the slope is positive/negative to know where it is increasing or decreasing but I don't really know where to start with problems with constants.

Hint: Take the derivative and make that greater than zero for all x in \(\displaystyle (-\infty,\, \infty)\)
 
Q. For what values of c is the function \(\displaystyle \, f(x)\, =\, cx\, +\, \dfrac{1}{x^2\, +\, 3}\,\) increasing on \(\displaystyle \, \left(-\infty,\, \infty\right)?\)

I know that in general you have to find out where the the slope is positive/negative to know where it is increasing or decreasing but I don't really know where to start with problems with constants.

Oh, and if you want
c > f(x)
it might be good to find the maximum of f(x)
 
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