Consider the function $f(x)=x |x|$.

a.) On the interval $(-\infty, 0), f''(x) =$

b.) On the interval $(0, \infty), f''(x) =$

Thus,

c.) On the interval $(-\infty, 0), f(x)$ is ? Concave up Concave down

d.) On the interval $(0, \infty), f(x)$ is ? Concave up Concave down

e.) Does $f''(0)$ exist? ? Yes No