What are the absolute extrema of f(x)= x^(2)+2/x on the interval [1,4]?

1 Answer

We need to find the critical values of f(x) in the interval [1,4].

Hence we calculate the roots of the first derivative so we have

(df)/dx=0=>2x-2/x^2=0=>2x^2(x-2)=0=>x=2

So f(2)=5

Also we find the values of f at the endpoints hence

f(1)=1+2=3

f(4)=16+2/4=16.5

The largest function value is at x=4 hence f(4)=16.5 is the absolute maximum for f in [1,4]

The smallest function value is at x=1 hence f(1)=3 is the absolute minimum for f in [1,4]

The graph of f in [1,4] is

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