Continuous? PLEASE HELP

[nikchic5]

Let f be the piecewise-defined function
f(x)= sin x if x is less than 0
and
f(x)=(x^3) + x if x is greater than or equal to 0


there are 4 parts....thanks so much
(a) state the domain of f
(b) state the set of x values on which f is continuous
(c) state the set of x values on which f is differentiable
(d) write f'(x) as a piecewise-definied function


THANK YOU SO SO SO SO MUCH!

 

[daon]

a) sin and polynomial functions have a domain of all real numbers
b), c) You should really be able to answer this. Just look at the definitions of continuous and differentiable. The answer will be expected in interval notation as the domain is all real numbers.
d) take their derivatives...

 

[nikchic5]

Ok...

ao a would be all real numbers and
(d) f(x)= sin x and f'(x)=cos x
f(x)= x^3 + x and f'(x)=3x^4 +1

Is that correct so far?

Thanks so much

 

[Gene]

Yes and no. You erred on d(x^3) and for completness you should specify where the derivitives apply.