Question

please help?
Let f(x)={x^2, x<1 ; 2x, x>1
a. find f'(x) for x<1
b. find f'(x) for x>1
c. find lim x→1^- f'(x)
d. find lim x→1^+ f'(x)

Answer 1

Do you need help to find f`(x)? It will have two parts too.

Answer 2

I can find f'(x)

Answer 3

What is the problem than?

Answer 4

the answer not going to be the same for all 4.

Answer 5

True it will depend where you are :)
What is the answer for a, and b, ?

Answer 6

a) 2x
b) 2
c) 2
d)2

Answer 7

thanks @eliassaab but I need to do work to.

Answer 8

\[
\lim_{x->1^-} 2 x =2\\
\lim_{x->1^+} 2 =2\\

\]

Answer 9

@eliassaab do you think you could help with these?
e. Does lim x→1 f'(x) exist? Explain/justify your answer.
f. Use the definition to find the left-handed derivative of f at x=1 if it exists.
g. Use the definition to find the right-handed derivative of f at x=1 if it exists.
h. Does f'(1) exist? Explain/justify your answer

Answer 10

also if it shows im not viewing this question, I am. im on mobile so its weird.

Answer 11

thank you so much!

Answer 12

YW

Answer 13

Wait, I need to do some corrections. Sorry.

Answer 14

e) yes since the right hand limit and the left hand limit exist and are equal
f) yes and it is equal to 2
g) yes and it is equal to 2
h) no because the function f is not continuous at x=1, so it cannot be differentiable at 1