Given `f(x)=(4x)/(x^2+1)`
Find the derivative using the Quotient Rule. The set the derivative equal to zero and solve for the critical x value(s).
`f'(x)=[(x^2+1)(4)-(4x)(2x)]/(x^2+1)=0`
`f'(x)=4x^2+4-8x^2=0`
`f'(x)=-4x^2+4=0`
`f('x)=-4(x^2-1)=0`
`x=1,x=-1`
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Given `f(x)=(4x)/(x^2+1)`
Find the derivative using the Quotient Rule. The set the derivative equal to zero and solve for the critical x value(s).
`f'(x)=[(x^2+1)(4)-(4x)(2x)]/(x^2+1)=0`
`f'(x)=4x^2+4-8x^2=0`
`f'(x)=-4x^2+4=0`
`f('x)=-4(x^2-1)=0`
`x=1,x=-1`