Question

I need help with 9 questions! @vocaloid

Answer 1

These are correct so far

Answer 2

@vocaloid

Answer 3

1 is d

Answer 4

3 is b

Answer 5

don't know 2

Answer 6

for the differentiable piecewise function it's only differentiable over the interval specified by the piecewise definition

so where x < 8 and x > 9 exclusive

Answer 7

I'm going in order of how I sent it not the number the attachment says

Answer 8

so is d correct?

Answer 9

ok

Answer 10

yeah nvm that's right

Answer 11

so d is correct?

Answer 12

is a the answer for 2
-6?

Answer 13

3 is b?

Answer 14

After these questions, I have 3 more and I promise that is all

Answer 15

gonna get a second opinion on the derivative questions on closed intervals

Answer 16

okay

Answer 17

If a function f is differentiable, is the function f continuous? If not, give a counterexample. Explain your answer.








do you know this?

Answer 18

If a function f is continuous, is the function f also differentiable? If not, give a counterexample. Explain your answer. or this?

Answer 19

being differentiable implies continuity but a continuous function is not necessarily differentiable (example: if it has a vertical tangent)

Answer 20

okay cool

Answer 21

alright I got a second opinion about "what is the derivative of f'(x) = x^2 over the closed interval [-3,3]"?

since there are no discontinuities the derivative is just taken normally to be 2x

Answer 22

okay cool and is 3 b?

Answer 23

yeah that's what i got too

Answer 24

\(\color{#0cbb34}{\text{Originally Posted by}}\) @Vocaloid
being differentiable implies continuity but a continuous function is not necessarily differentiable (example: if it has a vertical tangent)
\(\color{#0cbb34}{\text{End of Quote}}\)
is this for the first writing response or second?

Answer 25

it applies to both

If a function f is differentiable, is the function f continuous? If not, give a counterexample. Explain your answer. ---> being differentiable implies continuity

If a function f is continuous, is the function f also differentiable? If not, give a counterexample. Explain your answer. or this? ---> but a continuous function is not necessarily differentiable

Answer 26

for the counter-example you can use f(x) = |x| since it's continuous but not differentiable on x = 0

Answer 27

okay I wonder why we got 2 of basically the same question

Answer 28

they're not the same question

it's like the difference between "are all squares rectangles" or "are all rectangles squares" they're not asking the same thing and have different solutions

Answer 29

true just that this happens to have the same answer

Answer 30

If a function f is differentiable, is the function f continuous? ---> if a function is differentiable it must be continuous via the limit definition

If a function f is continuous, is the function f also differentiable? ---> if a function is continuous it may or may not be differentiable if it has an edge or vertical tangent

Answer 31

1 more question (multiple choice)

Answer 32

is b right for this one?

Answer 33

there's a discontinuity at x = 1 so changing it to (-10,14] still doesn't fix the problem so it's not differentiable there either

Answer 34

so e

Answer 35

plus it's not even defined from (-10 to 1)

so yeah I think E is the better choice

Answer 36

okay thank you so much for your help!