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$Use the function f (x) = x^{1 / x}, x > 0, to determine the bigger of the two$ $numbers e^{π} and π^{e} .$

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πe < eπ

πe > eπ

πe > 1

eπ < 1

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detailed solution

Correct option is B

f(x)=x1/x,(x>0)⇒ f′(x)=x1/x(1−1nx)x2=0⇒x=e⇒ f'(x) ≤ 0, when x ≥e⇒ f(x) decreases when x ≥e And f′(x)>0, when 0e⇒ f(π)eπ

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Use the function f(x)=x1/x,x>0, to determine the bigger of the two numbers eπ and πe.

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

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$Use the function f (x) = x^{1 / x}, x > 0, to determine the bigger of the two$ $numbers e^{π} and π^{e} .$