For a differentiable function f(x), which of the following are true for only x=a?

I. lim f(x) as x approaches a- = lim f(x) as x approaches a+
II. lim f(x) as x approaches a = f(a)
III. f'(a-) = f'(a+)
IV. f(a) = f'(a)

a. I and III only (not this one)
b. II and IV only
c. I, II, and III only
d. III only
e. I, II, III, IV

Question

For a differentiable function f(x), which of the following are true for only x=a?

I. lim f(x) as x approaches a- = lim f(x) as x approaches a+
II. lim f(x) as x approaches a = f(a)
III. f'(a-) = f'(a+)
IV. f(a) = f'(a)

a. I and III only (not this one)
b. II and IV only
c. I, II, and III only
d. III only
e. I, II, III, IV

anonymous · Answer

i think its C

anonymous · Answer

coz considering the functions as diff. make it continuos

anonymous · Answer

that will satisfy 1 and 2 statements and third is the result of 1st

anonymous · Answer

got that...? @SinoatrialMath

anonymous · Answer

That makes sense - I thought it was I and III but II also fits (the correlation between derivative and limit slipped my mind). Thanks a lot!

anonymous · Answer

no prob.. :)