3. -/1 points details my notes scalc9 3.1.030. find the critical numbers of the function. (enter your…

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:

$5,-5$