math, Calculus

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Find the relative extrema of the functions.

f(x)=4x/(x^2+1)

f(x)=1/(x-2)

take the derivative, set to zero.

the first as an example:

f(x)= 4x (x^2 +1)^-1

f'(x)= 4 (x^2 +1)^-1 -4x(2x)(x^2 +1)^-2
set to zero. Multiply through by (x^2+1)^2

0=4(x^2+1) - 8x^2
4x^2=1
x= +- 1/2

what about the second question
f(x)1/(x-2)

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