3. -/1 points details my notes scalc9 3.1.030...
3. -/1 points details my notes scalc9 3.1.030. find the critical numbers of the function. (enter your answers as a comma - separated list. if an answer does not exist, enter dne.) g(v)=v^3 - 75v + 7 v =
Answer
# Explanation:
## Step1: Find the derivative
Differentiate $g(v)=v^{3}-75v + 7$ using the power - rule. The derivative $g'(v)=3v^{2}-75$.
## Step2: Set the derivative equal to zero
Set $g'(v) = 0$, so $3v^{2}-75=0$. First, factor out a 3: $3(v^{2}-25)=0$. Then, since $v^{2}-25=(v - 5)(v + 5)$, we have $3(v - 5)(v + 5)=0$.
## Step3: Solve for v
Set each factor equal to zero. If $v-5=0$, then $v = 5$; if $v + 5=0$, then $v=-5$.
# Answer:
$5,-5$