# What are the critical values of #f(x)=x/e^(x+x^2)-x^2#?

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To find the critical values of ( f(x) = \frac{x}{e^{x + x^2}} - x^2 ), we need to first find the derivative ( f'(x) ) and then set it equal to zero to solve for critical points.

[ f'(x) = \frac{1}{e^{x + x^2}} - 2x ]

Next, set ( f'(x) = 0 ) and solve for ( x ):

[ \frac{1}{e^{x + x^2}} - 2x = 0 ] [ \frac{1}{e^{x + x^2}} = 2x ] [ e^{x + x^2} = \frac{1}{2x} ] [ x + x^2 = \ln\left(\frac{1}{2x}\right) ]

This equation can be solved numerically or graphically to find the critical values of ( x ).

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