Find the value of x for which the function f(x) = x/2+2/x !=0 is stric

1.	Find the value of x for which the function f(x) = x/2+2/x !=0 is strictly increasing or strictlydecreasing.
Answer» GIVEN function is f(x) = x/2 +2/x so, f'(x) = 2(-1/x²) +1/2 = 1/2-2/x² for the function to be strictly increasing f'(x) >0 => 1/2-2/x² >0=> 1/2> 2/x² => x²> 4 ..... so x belongs to (-∞,-2) U (2,∞) and hence it will be strictly decreasing in (-2,2)

Find the value of x for which the function f(x) = x/2+2/x !=0 is strictly increasing or strictlydecreasing.

Answer»

GIVEN function is f(x) = x/2 +2/x

so, f'(x) = 2(-1/x²) +1/2 = 1/2-2/x²

for the function to be strictly increasing

f'(x) >0 => 1/2-2/x² >0=> 1/2> 2/x² => x²> 4 ..... so x belongs to (-∞,-2) U (2,∞)

and hence it will be strictly decreasing in (-2,2)