Question

how do you find the maximum and minimum values of f(x)=x^3-6x^2-63x+2?

Answer 1

you have to find the derivative. Get critical points and use those to get your max and min. and concavity and points of inflection are found with the 2nd derivative

Answer 2

okay so I have two critical points, so how do i use those to get the max and min values?

Answer 3

were you given an interval where the max and min values were to be found?

Answer 4

because f(x) -> +-infinity for x->+-infinity

Answer 5

To find all local maxima and local minima, compute the first derivative the given function and
set it equal to 0,
and solve for x.

Answer 6

ya the interval is [-4,0]

Answer 7

f'(x)=3x^2-12x-63

Answer 8

putting f'(X)=0.we get

Answer 9

x=7 and -3

Answer 10

good, now check the f(x) values for those x's

Answer 11

the highest one is your max and the lowest one is you min

Answer 12

your*

Answer 13

x=7 and x=-3.

Answer 14

where does the given interval come in?

Answer 15

if you didn't have an interval, then f(x) would not have a defined maximum and minimum, since it would just keep rising/falling as you increase/decrease x

Answer 16

a function where this is not the case could be cos(x), which has its maximum at 1 and minimum at -1, without an interval. Try drawing the graphs, then you will see

Answer 17

Please go through it.

Answer 18

it looks good, except for the graph, it's not the right function

Answer 19

it should look something like that

Answer 20

it should be quite clear that there are two local extrema

Answer 21

Please see it.

Answer 22

i mean, it should be quite from your graph

Answer 23

perfect

Answer 24

Thank you