Published by:
CGP EDU Academic Team
Published on: August 11, 2026
Using calculus prove that 
for positive real numbers.
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
Let f(x) = λ nx ⇒ f "(x) = 
So 
for x 1 , x 2 , .......... , x n ∈ R +
⇒ 
⇒ 
⇒ G.M. A.M.
Again
⇒ 
⇒ 
(x 1 x 2 ...... x n ) 1/n
⇒ G.M. ≤ A.M.
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems
If f(x) = cos π x + 10x + 3x 2 + x 3 , – 2 ≤ x ≤ 3 then absolute minimum value of f(x) is-
The function f(x) = x 5 – 5x 4 + 5x 3 – 1 has-
The function f(x) = has no extrema. if (n ∈ z)
If x exceeds by its square by the greatest possible quantity then x is-
An extreme value of the function
f(x) = (sin –1 x) 3 + (cos –1 x) 3 (–1 < x < 1) is
Let f(x) = (t + 4) 4 log (t+ 1) dt, then -