Thread: mean value theorem

Use the Mean Value Theorem to prove that sqrt(1+x) < 1 + x/2 for all x > 0. Generalize this result to the function (1+x)^r, where r < 1 is a positive rational number.

Thanks!

Originally Posted by friday616

Use the Mean Value Theorem to prove that sqrt(1+x) < 1 + x/2 for all x > 0. Generalize this result to the function (1+x)^r, where r < 1 is a positive rational number.

Thanks!

Using the MVT, for some .

. For , .

Thus,

for

as desired.

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Using the same method, see if you can generalize that result.