1. ## Critical Points

How many critical points does the function f(x)=(x-2)^5(x+3)^4 have?
The answer is supposed to be 3.
I'm having major issues with this problem. I know how to find critical points, but I'm actually having more trouble expanding the equations and such.
I will be incredibly grateful to anybody willing to lend me a hand. Thanks!

2. To find the critical points of any equation you must take the derivative of the function. So by expanding the equation you are creating more trouble for yourself than is needed. In this case you need to perform the Product Rule for the entire equation while utilizing two separate Chain Rules for the quantities involved.

3. Just to add...if you did want to expand that equation, you can use the binomial theorem.

4. Originally Posted by mech.engineer.major
To find the critical points of any equation you must take the derivative of the function. So by expanding the equation you are creating more trouble for yourself than is needed. In this case you need to perform the Product Rule for the entire equation while utilizing two separate Chain Rules for the quantities involved.
Yeah, I've tried that, but I'm messing up my math somewhere.

5. Factoring is an excellent method for this type of problem. It may be hard to see but it is very possible that you can factor out entire quantities after you have performed the Product Rule with the Chain Rules. Show your work until the point where you got stuck.

6. You have a product of two functions of functions of x. Use the product rule. Also, these function of x must be differentiated using the chain rule!