Tutonis Exercise
Find the critical numbers of the function.

Step 1
To find the critical numbers of , you must find all -values for which or Select

Ask by Lowe Graham. in the United States

Mar 31,2025

Question

Tutonis Exercise
Find the critical numbers of the function.

Step 1
To find the critical numbers of , you must find all -values for which or Select

Ask by Lowe Graham. in the United States

Mar 31,2025

UpStudy AI · Accepted Answer

1. **Differentiate the function.**  
   Given $$ f(x)=7x^2-4x $$, compute the derivative:
   $$
   f'(x)=\frac{d}{dx}\left(7x^2-4x\right)=14x-4.
   $$

2. **Set the derivative equal to zero to find critical numbers.**  
   Solve:
   $$
   14x-4=0.
   $$

3. **Solve for $$ x $$.**  
   Add $$ 4 $$ to both sides:
   $$
   14x=4,
   $$
   and then divide by $$ 14 $$:
   $$
   x=\frac{4}{14}=\frac{2}{7}.
   $$

Since $$ f $$ is defined for all real numbers and $$ f'(x) $$ exists for all $$ x $$, the only critical number is $$ x=\frac{2}{7} $$.
The critical number of the function $$ f(x)=7x^2-4x $$ is $$ x=\frac{2}{7} $$.

Tutonis Exercise
Find the critical numbers of the function.

Step 1
To find the critical numbers of , you must find all -values for which or Select

Solución de inteligencia artificial de Upstudy

Responder

Solución

Beyond the Answer

preguntas relacionadas

Latest Calculus Questions

Tutonis Exercise Find the critical numbers of the function. Step 1 To find the critical numbers of , you must find all -values for which or Select

Solución de inteligencia artificial de Upstudy

Responder

Solución

Beyond the Answer

preguntas relacionadas

Latest Calculus Questions

Tutonis Exercise
Find the critical numbers of the function.

Step 1
To find the critical numbers of , you must find all -values for which or Select