The answer is NOT correct.
Find the positive critical point of the function

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Ask by Lewis Davison. in the United States

Mar 28,2025

Question

The answer is NOT correct. Find the positive critical point of the function $$ f(x)=\frac{x}{x^{10}+6} $$ $$ x=0.946 $$ Preview Mv Answore

UpStudy AI · Accepted Answer

To find the positive critical point of the function $$ f(x) = \frac{x}{x^{10}+6} $$, we need to find the value of $$ x $$ where the derivative of the function is equal to zero.

First, let's find the derivative of the function $$ f(x) $$ with respect to $$ x $$ using the quotient rule:

$$ f'(x) = \frac{(x^{10}+6)(1) - x(10x^9)}{(x^{10}+6)^2} $$

Now, we need to set the derivative equal to zero and solve for $$ x $$:

$$ \frac{(x^{10}+6)(1) - x(10x^9)}{(x^{10}+6)^2} = 0 $$

Simplifying the equation:

$$ (x^{10}+6)(1) - x(10x^9) = 0 $$

$$ x^{10} + 6 - 10x^{10} = 0 $$

$$ -9x^{10} + 6 = 0 $$

$$ -9x^{10} = -6 $$

$$ x^{10} = \frac{6}{9} $$

$$ x^{10} = \frac{2}{3} $$

Taking the tenth root of both sides:

$$ x = \sqrt[10]{\frac{2}{3}} $$

$$ x \approx 0.946 $$

Therefore, the positive critical point of the function $$ f(x) = \frac{x}{x^{10}+6} $$ is approximately $$ x = 0.946 $$.
The positive critical point of the function $$ f(x) = \frac{x}{x^{10}+6} $$ is approximately $$ x = 0.946 $$.

The answer is NOT correct.
Find the positive critical point of the function

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