Question

Find the value f ' (0) to determine if f(x) is differentiable at x=0

Answer 1

\[f(x)=x ^{1/3}+2\]

Answer 2

ok first I was asked to graph the function
second I was asked if f(x) is continuous at x=0

Answer 3

so I did the graph, no problem
yes f(x) is continuous at x=0

Answer 4

I took the derivative and the derivative should be undefined

Answer 5

is f continuous at 0?
or is f right continuous at 0?

Answer 6

what do you mean f right continuous at o?

Answer 7

isn't actually left continuous nothing exists to the left


for it to be continuous at x=a you must have:
1)\[\lim_{x \rightarrow a}f(x) \text{ exists }\]
2) \[f(a) \text{ exists }\]
finally
3) \[\lim_{x \rightarrow a} f(x)=f(a)\]


can you answer number 1?

Answer 8

oh is that not a 1/2 power?

Answer 9

I cannot read latex I swear

Answer 10

3 and 2 look like

Answer 11

http://www.wolframalpha.com/input/?i=graph+x%5E%281%2F3%29+%2B+2&a=%5E_Real

Answer 12

the power is (1/3-1)

Answer 13

but also song that does not give f' is 0 at x=0


\[\frac{1}{3x^\frac{2}{3}}\]

Answer 14

I thought I was looking at the wrong graph

Answer 15

it is x to the (1/3) power plus 2

Answer 16

Yea sorry @precal I thought I was seeing 1/2 not 1/3 :(
my bad

Answer 17

i have to take my cat to the vet
i will bb

Answer 18

ok here is where I got very confused. I did this by hand and then I used my graphing calculator to verify the solution
and it gave me 100
well that is very confusing or maybe I found a function where the calculator gives an incorrect solution

Answer 19

thanks @myininaya hope your cat feels better. Mine never like going to the vet. She did live for about 20 years. The best cat ever.....

Answer 20

the first thing is need to prove (right =left ) continuous ,and then diferenationate

Answer 21

well the f(0)=2 the point exists, and the limit exists at 2 approaching zero from both sides

Answer 22

yes

Answer 23

no f ' (0) does not equal zero
that implies that f ' (0) has a horizontal tangent at x=0 and it clearly does not

Answer 24

this is the graph of the derivative