Let f be the real-valued function defined by f(x)=sin^3(x)+sin^3(|x|)
a. Find f '(x) for x>0
b. Find f '(x) for x<0
c. Determine whether f9s0 is continuous x = 0. Justify your answer.
d. Determine whether the derivative of f(x) exists at x=0. Justify your answer
Thanks a lot for the help, I had a lot of trouble throwing the absolute value into the derivative.
Hint: What is the value of f(x) when x is negative? What is the value of f(x) when x is positive? Then construct f(x) as a piece-wise function and take the derivative of each piece. (Note: f'(x) is NOT defined at x = 0!)
Originally Posted by aussiekid90