Find the points of local maxima or local minima, if any, of the following function, using the first derivative test. Also, find the local maximum or local minimum values, as the case may be: `f(x)=x/2+2/x ,x >0`

Explanation

`f(x)= x/2+ 2/x ,x>0`

`f ′(x)= 1/2− 2/(2x^2)`
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⇒f ′ (x)=0

`⇒1/2​ − (2)/(2x^2)`=0

`⇒x^2 =4`

x=±2

at x=−2,f(x) has local maxima

`f(−2)= −2/2 + 2/-2 =-2`
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