Question

Find the minimum value of X^50+50/x..............please solve this......​

Answer 1

use ap,GP ap>_gp a=x^49,b=50/x

Answer 2

We have to find the minimum value of x⁵⁰ + 50/x

solution : here f(x) = x⁵⁰ + 50/x

differentiating with respect to x,

f'(x) = 50x^49 - 50/x²

At f'(x) = 0, 50x^49 - 50/x² = 0 ⇒x = 1

Again differentiating with respect to x,

f"(x) = 50 × 49x^48 + 50 × 2/x³

at x = 1 , f"(x) > 0

So, at x = 1 f(x) get the minimum value.

Therefore the minimum value of x⁵⁰ + 50/x = 1⁵⁰ + 50/1 = 51

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