Critical numbers, max & mins? Help:(

[OhhCalculus]

Soo, I have a test tomorrow, and I've been studying hardcore, but there's 3 (out of the 20!) problems that have me stumped. Any help is greatly appreciated.

1. Find the absolute or local maximum and minimum of f(x)=8-2x if x is greater than or equal to 6
2. Find the critical numbers of f(x)=x^4(x-3)^3
3. Find the maximum or minimum of F(x)=(1-x^2)+6x^2

 

[lookagain]

You didn't show any work on these three problems for us to see, and you allege that 17 out of 20 problems
do not have you stumped. What's to say that these three problems aren't all of your problems?

 

[galactus]

Only 3 out of 20!?. 3 out of 2432902008176640000?.

Wow, that's a lot of problems. Only these 3 have you stumped. That's pretty good.

This instructor sure piles on the homework. :wink:

#2; you could expand out and rewrite as \(\displaystyle x^{7}-9x^{6}+27x^{5}-27x^{4}\).

Differentiate term by term.

Or, you could use the product rule as is:

\(\displaystyle x^{4}\cdot 3(x-3)^{2}+(x-3)^{3}\cdot 4x^{3}\)

Now, factor and you should be able to find the critical points.