Find extrema of `f(x) = (x^2+4)/(2x+3)` . Draw graph of `g(x) = 1/(f(x))` and comment on its local and global extrema.

Explanation

`f(x) =(2(x^(2)+3x-4))/((2x+3)^(2)) =(2(x+4)(x-1))/((2x+3)^(2))=0`

Local minima occurs at x=-4
local maxima occurs at x=1
`g(x) =(1)/(f(x)) =((2x+3)/(x^(2)+4))`
`g'(x) =(-2(x +4)(x-1))/((x^(2) +4)^(2))`
local maxima at x=-4
local minima at x=1
global maxima & minima do not exists