Question 997691
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1) &nbsp;<A HREF=http://imgur.com/k4hAlxI>http://imgur.com/k4hAlxI</A> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;



k(x) = {{{1/(x^2+5)}}}.


k(x) = {{{(x^2+5)^(-2)}}},


k'(x) = {{{(-2)}}}.{{{(x^2+5)^(-3)}}}.{{{2x}}}

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{{{graph( 250, 250, -3.5, 3.5, -1.1, 1.5,
          1/(x^2+5)
)}}}


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Plot &nbsp;{{{1/(x^2+5)}}} 

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k'(x) &nbsp;is positive at &nbsp;x < 0 &nbsp;and is negative at &nbsp;x > 0.


k(x) &nbsp;is increasing in the interval &nbsp;({{{-infinity}}}, {{{0}}}]. 

k(x) &nbsp;is decreasing in the interval &nbsp;[{{{0}}}, {{{infinity}}}).