Question

Please help me with prime graph question!

Answer 1

Use the figure below to estimate the indicated derivatives. If a derivative does not exist, enter dne in the answer blank. The graph of f(x) is black and has a sharp corner at x=2. The graph of g(x) is blue

Answer 2

f'(x)=1
f'(x)=2
f'(x)=3

Answer 3

@tkhunny

Answer 4

We probably should start with this:
The derivative of f(x) does not exist at x = 0, 2, 4
The derivative of g(x) does not exist at x = 0, 4

Answer 5

Yes, I understand so far

Answer 6

so whenever point is hit the line, its not exist

Answer 7

The rest is eyeball! Just write down the answers! Everything is linear.

f'(1)= 1
f'(2)= dne
f'(3)= -1

I'm not quite sure what this means:

f'(x)=1
f'(x)=2
f'(x)=3

Answer 8

sorry i forgot to write.
it says Let j(x)=g(x)f(x). Find

Answer 9

We probably should start with this:
The derivative of j(x) does not exist at x = 0, 2, 4

You fill in the blanks

j'(0) =
j'(1) =
j'(2) =
j'(3) =
j'(4) =

Answer 10

Im confused, theres no graph j(x). How do i find out

Answer 11

Multiplication Rule: j'(x) = f(x)g'(x) + g(x)f'(x)

Answer 12

ok, how do i find g'(x) f'(x)?

Answer 13

Just look at it.

f'(x) = 1 on (0,2)
f'(x) = -1 on (2,4)
g'(x) = -1/2 on (0,4)