Find where the maxima and minima of the function f(x)=2x / (x^2+3) occur ?
1 Answer | Add Yours
We are given the function f(x) = (2*x)/(x^2+3).
We calculate the absolute minimum and and the absolute maximum as follows. First find the differential of the function.
f(x) = (2*x)/(x^2+3).
=> f'(x) = 2/(x^2 +3) - 4x^2 /( x^2 + 3)^2
Now equate this to zero.
2/(x^2 +3) - 4x^2 /( x^2 + 3)^2 = 0
=> 2*( x^2 + 3) - 4x^2 = 0
=> 2x^2 + 6 - 4x^2 =0
=> 2x^2 = 6
=> x^2 = 3
=> x = -sqrt 3 and + sqrt 3
We have the minima at x= -sqrt 3 and the maxima at x =sqrt 3.
Join to answer this question
Join a community of thousands of dedicated teachers and students.Join eNotes