Question

Continuity/differentiability question on graphs

Answer 1

i do not know how to find part (iii) and unsure of part (ii)

Answer 2

Normally, if you're just given the graph, you can't find derivatives (at least, their precise value)

But would it help you to know that \(\large \sqrt 3 \approx 1.732\) ?

Meaning it's between 1 and 2...

Answer 3

well yea, so u mean i shd just estimate the y value?

Answer 4

dy/dx equals to the m in y=mx+c so u can calculate m and find f`

Answer 5

Not that, put it this way, on the interval (1,2) the function is practically linear, so the derivative of any f in that interval is simply the slope of the line... which is...?

Answer 6

By the way, if you really want to be formal, then
\[\Large 1 < 3 < 4 \implies \sqrt1 <\sqrt 3 <\sqrt 4 \implies 1 < \sqrt3 < 2\]

Answer 7

ah! -1?

Answer 8

YES, precisely ^_^

Answer 9

omggg i almost forgot about that, thanks!

Answer 10

part iv good too?

Answer 11

lol thats wht i said too. :p

Answer 12

part (iv) is x=0 coz its a min

Answer 13

x=3 i mean

Answer 14

Okay, good.

Answer 15

wat do u get for ii

Answer 16

(2,2), (2,1.5),(2,1),(2,0.5)(2,0) i am not sure

Answer 17

I think 'points' in this case just means values of x for which f(x) is not differentiable...

Answer 18

And what's so special about (2 , 0.5) ?

Answer 19

few of the points u listed dont even exist on graph,
so dont list them..

Answer 20

i think it would be x =1

Answer 21

haha, idk, so if its x value then it should be x=2?

Answer 22

x=1 and x=2

Answer 23

ya it doesnt exist thats why not differentiable? haha

Answer 24

why x=1 included?

Answer 25

if it doesnt exist in domain, dont wry about it

Answer 26

roughly speaking, the function isn't differentiable at points where:

\(\color{green}{\checkmark }\) It is not continuous
\(\color{green}{\checkmark }\) It makes a rather -sharp- turn, (IE, not smooth)

Answer 27

i see, okay i'll take note of that, thanks guys!(:

Answer 28

Show that you've taken note of it:
for what values of x is the function not differentiable?
(your final answer)

Answer 29

x=1 and x=2, x=1 is sharp turn, x=2 is not continuous

Answer 30

Correct,

also,
at x=1, left slope(-infinity ? ) \(\ne\) right slope (-1)

Answer 31

^ oh ya thats true so limits from left/right are not the same which make it discontinuous.

Answer 32

at x = 2, its discontinuous cuz, left limit \(\ne\) right limit
at x=1, its not differentiable cuz, left slope \(\ne\) right slope

Answer 33

if ur teacher wants points, just give her that :-
At points (1, 1) and (2, 1) on graph, the graph is not differentiable

Answer 34

*function is not..

Answer 35

okay thanks! :D

Answer 36

np :)