Question

Help I don't know where to start
The graph in the picture is of the derivative of the function f(t).
Given that f(0)=20, estimate of the maximum value of f(t).

Answer 1

@satellite73 can you please help me

Answer 2

you'll need to integrate this to get the function. notice that you have the two zeros of x = 0 and x = 6.

so f'(t) = -x(x-6), f'(t)= -x^2 - 6x
now you should be able to integrate and find the max value

Answer 3

yeah we can do this, but first i think you need an estimate of the area under the curve

Answer 4

ok so the area is 114

Answer 5

is that right

Answer 6

are you still there

Answer 7

I am wondering if this is a trick question? you get a cubic, which goes to infinity.
you do get a local maximum. Is that what they are asking for ?

Answer 8

the leading coefficient is not minus one in this case

Answer 9

there are two tails, one goes down, the other up

Answer 10

I am really confussed I wrote the problem exactly as it says

Answer 11

it is asking for the max on the interval i think

Answer 12

the function is not presumed to exist outside of this interval

Answer 13

ok so then how do I get the estimate

Answer 14

are yall still there

Answer 15

yes, i am here and i am thinking

Answer 16

ok

Answer 17

The way I did it was integrate -x(x-6) dx
and use f(0)=20 to define the constant

Answer 18

ok then what

Answer 19

@phi this might work, but you are making an assumption
namely that this is \(-x^2+6x\) and not \(-ax^2+6ax\)

Answer 20

so then how do you answer the question

Answer 21

still thinking

Answer 22

I hate to rush you but I got to get this done I am on a time limit

Answer 23

got an example in the book?

Answer 24

no

Answer 25

my book is worth lesss

Answer 26

yes, it should be -15/4 * x(x-6)
to match y=30 at x=2

Answer 27

ok I am following

Answer 28

what next

Answer 29

integrate -15/4 x^2 + 45/2 x

Answer 30

ok

Answer 31

I got -520.86

Answer 32

now what

Answer 33

you get -15/4 * x^3/3 + 45/4 x^2
add 20 to get
y= -15/4 * x^3/3 + 45/4 x^2 +20

evaluate at x=0 to get 20
and at x=6 to get ?

Answer 34

-500.86

Answer 35

just wondering where the \(-\frac{15}{4}\) came from?

Answer 36

-15/4 came from y' graph. it is a parabola and it goes through (2,30)

Answer 37

is my answer right?

Answer 38

oh ok
i think you are supposed to estimate the area under the curve and add 20 to the result, but this method is probably better

Answer 39

is my answer right?????

Answer 40

no, I think they want you to find the area under the curve.
and add the constant. It seems faster..

Answer 41

what is the area then

Answer 42

i get 155

Answer 43

ok that is what I got 2

Answer 44

so then take the -500.86 +155

Answer 45

lol then go with that one,
@phi did you get that too?

Answer 46

no just 155 that is the answer

Answer 47

so then all O should write is 155+20=175 and that is my answer?

Answer 48

the integral is 155. (that includes the 20 already)

Answer 49

oh ok so then is 155 my final answer

Answer 50

is it?

Answer 51

yes. if you count the area under f' more carefully you get about 135
add to get about 155

Answer 52

**add 20

Answer 53

ok yup I got it then thanks