(1 point)
Find all critical points of the function . If there is more than one critical point, list them in descending order and separate them by
commas.
The critical point(s) is(are)

Ask by Ryan Christensen. in the United States

Mar 28,2025

Question

(1 point)
Find all critical points of the function . If there is more than one critical point, list them in descending order and separate them by
commas.
The critical point(s) is(are)

Ask by Ryan Christensen. in the United States

Mar 28,2025

UpStudy AI · Accepted Answer

Let $$ f(x)=x\ln(6x) $$. The derivative of $$ f(x) $$ is:
$$
f'(x)=\ln(6x)+1
$$

Set $$ f'(x)=0 $$:
$$
\ln(6x)+1=0 \quad \Longrightarrow \quad \ln(6x)=-1
$$

Exponentiating both sides gives:
$$
6x=e^{-1}
$$

Solving for $$ x $$:
$$
x=\frac{e^{-1}}{6}=\frac{1}{6e}
$$

Thus, the only critical point is:
$$
\frac{1}{6e}
$$
The critical point is $$ \frac{1}{6e} $$.