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Calculus Level 2

Find the largest number among the following : $\color{#20A900}{\sqrt [1]{1},\sqrt [2]{2},\sqrt [3]{3},\sqrt [4]{4},\sqrt [5]{5},\sqrt [6]{6},\sqrt [7]{7}}$ If the largest number is of the form $\sqrt [n]{n}$ , enter the value of $n+n$ .

The answer is 6.

1 solution

Hjalmar Orellana Soto
Nov 12, 2015

Let $f$ be a function such that $f(x)=\sqrt[x]{x} \rightarrow f'(x)=\sqrt[x]{x}(\frac{1-\ln x}{x^{2}})$ . In the maximum value of $f$ we know $f'(x)=0$ . This means the maximum value of $f$ gets for $x=e$ and the closer number to $e$ is $3$

You need to prove that $f''(x) < 0$ to prove that it's a maximum point.

Pi Han Goh - 5 years, 6 months ago

I know, but, knowing the graph, that's needless

Hjalmar Orellana Soto - 5 years, 6 months ago

Where's the graph?

Pi Han Goh - 5 years, 6 months ago

@Pi Han Goh – well, I didn't drew it, only knew it before, sorry about

Hjalmar Orellana Soto - 5 years, 6 months ago

Get rid of your calculator

The answer is 6.

1 solution

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