Question

find the critical numbers of the function f(x)= x^6(x-4)^5

Answer 1

i found the derivative of the dunctions (x-4)^4(x^5)(11x-24)

Answer 2

and than equating f'(x)=0

Answer 3

x=4 , 0 , 24/11

Answer 4

yep!

Answer 5

but i also have to describe the behavior at the critical points

Answer 6

whether it has a maximum or minimum

Answer 7

at x=4 would it be minimum?

Answer 8

Since you are given a graph you don't actually need to find g''
just look at small intervals around those critical numbers
do those critical numbers stand higher or lower on those sub-intervals

Answer 9

or f'' (not g'') sorry

Answer 10

no i had to draw the graph

Answer 11

Well if that is a correct graph, can you tell which or mins and maxs (locally)?

And then we can also determine this without a graph too

Answer 12

would 4 be min?

Answer 13

yes because looking at its near neighborhoods he is the lowest around them

Answer 14

the other critical points arent maximum right?

Answer 15

is 0 local maximum?

Answer 16

it seems she as graphed f'(x) @myininaya

Answer 17

yea i did graph f'(x)

Answer 18

just a clarifying question, do you say below point a minimum ?