What are the critical points of #s(t)=(e^t-2)^4(e^t+7)^5#?
This is one of those crazy product rule problems where you have to patiently apply the product rule and then factor out all of the common terms: you should end up with
Now the last 'term' simplifies to
Soooooo...the only time the equation can be zero is when
If you graph this monstrosity with a very high y max, you will see the function has a minimum at