Question

can anyone help with this. I tried it but i don't know if I'm doing it right ..

Answer 1

youre on the right track, i see you made rectangles and triangles to define areas with

Answer 2

the area between f and the x axis is positive when above it, and negative below it, thats the only caveat you might want to consider

Answer 3

okay yes i know that but how would i find what the little f is. like f(6) and f'(5)... and then how do I know when big F is increasing or decreasing..

Answer 4

you have the graph of the function of little f, so what is the value of little f when x=6?

Answer 5

uhm 3?

Answer 6

F(x) is the area from 0 to x

f(x) is the value of the line of f at x

f'(x) is the slope of the graph of little f, at x

Answer 7

when x=6, it looks to me like f=0

Answer 8

count over 6 tics to the right, the line appears to be going thru the x axis

Answer 9

oh okay so f(6)= 0?

Answer 10

F(5) = 6, since the first 3 tics are equal, but opposite in area they cancel out, leaving 2 by 3

Answer 11

okay so then is f'(5) = 3

Answer 12

0 to 3 = 0
3 to 5 = 2 x 3 = 6
5 to 7 = 0

so ...

the slope of a line is y/x not x/y

Answer 13

f'(5)

notice that we have a corner when x=5

the slope on the left of 5 is 0, the slope on the right is not 0

the derivative is only defined when the slope from the right and left are the same.

Answer 14

the derivative of a function is defined as a limit, and in order for a limit to be defined it has to be the same from all approaches. in this case from the left and the right.

Answer 15

okay uhm I'm sort of confused tho. I found F(0) and f(5) by finding the area. so how do i find f(6) ?

Answer 16

@amistre64

Answer 17

this lag is killing my performance :/

Answer 18

things to keep in mind

F is defined by area

f is defined by the position of the graph

f' is defined by the slope of the graph

f(6) is the value of the graph when x=6

Answer 19

okay so f(6)= 0 & f'(5)= -3?

Answer 20

f' is only definable of the slope is the same on the left and the right; is the slope the same from left and right? or different?

Answer 21

uhm different... wait since there is a corner there wouldn't that make it a zero..?

Answer 22

zero is a definable slope, since 0 is a value that has meaning.

undefined, or does not exist are the proper answers to an unworkable slope

Answer 23

corners and sharp points in general will never have a definable slope at that point since they have different slopes on the left and right

Answer 24

so f'(5) is undefined..?

Answer 25

correct

Answer 26

okay thank you. can you just tell me if I'm correct for F(5) & F(7)?

Answer 27

for F(5) i got 21, and for F(7) i got 33

Answer 28

youve done thos incorrectly

F(3) is the area from x=0 to 3, half is under the x axis, half is over. equal parts that are opposites. F(3) = 0

F(5) = F(3) + (area from 3 to 5)

2x3 = 6 so the value of F(5) = 0 + 6

Answer 29

now,

F(7) = F(5) + (area from 5 to 7)

the area from 5 to 7, half over and half under, so equal parts that are opposite cancel out

F(7) = F(5) + 0

Answer 30

your error was in making all areas positive in value. over and under you made positive.

over the x axis is positive value
under the x axis is negative value

Answer 31

F(5) = -a+a+b = b

F(7) = -a+a+b+c-c = b

Answer 32

ohh okay so F(7) =12

Answer 33

oh so then it is 6..

Answer 34

the area of b = 2*3 = 6, not 12