question 5 of 10, step 1 of 2 correct consider the function: f(x)=(9x² - 100)/x step 1 of 2: find the…

question 5 of 10, step 1 of 2 correct consider the function: f(x)=(9x² - 100)/x step 1 of 2: find the critical values of the function. separate multiple answers with commas. answer how to enter your answer (opens in new window) selecting a radio button will replace the entered answer value(s) with the radio button value. if the radio button is not selected, the entered answer is used. x = none

question 5 of 10, step 1 of 2 correct consider the function: f(x)=(9x² - 100)/x step 1 of 2: find the critical values of the function. separate multiple answers with commas. answer how to enter your answer (opens in new window) selecting a radio button will replace the entered answer value(s) with the radio button value. if the radio button is not selected, the entered answer is used. x = none

Answer

Explanation:

Step1: Rewrite the function

Rewrite $f(x)=\frac{9x^{2}-100}{x}$ as $f(x)=9x - \frac{100}{x}=9x-100x^{-1}$.

Step2: Find the derivative

Using the power - rule $(x^n)'=nx^{n - 1}$, the derivative $f'(x)=(9x-100x^{-1})'=9 + 100x^{-2}=9+\frac{100}{x^{2}}$.

Step3: Set the derivative equal to zero

Set $f'(x)=0$, so $9+\frac{100}{x^{2}} = 0$. Then $\frac{100}{x^{2}}=-9$. Since the left - hand side $\frac{100}{x^{2}}>0$ for all non - zero real $x$, there are no solutions from $f'(x) = 0$.

Step4: Find where the derivative is undefined

The derivative $f'(x)=9+\frac{100}{x^{2}}$ is undefined when $x = 0$. But the original function $f(x)=\frac{9x^{2}-100}{x}$ is also undefined at $x = 0$.

Answer:

None