Question

Please check my work. Critical points.

Answer 1

@jim_thompson5910 have time? :) just want to double check everything.

Answer 2

sorry it's so dark D:

Answer 3

Neat writing

Answer 4

Critical points \[\large \checkmark \]

Answer 5

Aw thanks. If only nice writing got me extra credit ;)

Answer 6

for #1, I would have these additional steps

-(3x+1)(x-3) = 0
3x+1 = 0 or x-3 = 0
3x = -1 or x = 3
x = -1/3 or x = 3

but other than that, #1 looks good

Answer 7

ok :) I put that in on the side.

Answer 8

thanks!

Answer 9

Second one looks good

Answer 10

for part b), you have to make sure that the critical points lead to local extrema. Sometimes the critical points lead to saddle points which aren't extrema at all. In this case, you don't have to worry about it but it's always good to check

Answer 11

Good point jim

Answer 12

but you have the correct absolute extrema

Answer 13

oh wow. thanks. I hadn't thought about that!! I will check for sure.
excellent.