Suppose f(x)= |x^(2)+2x−63|.

Where is f(x) not differentiable?

2 answers

f(x) = |(x+9)(x-7)|

the function y = (x+9)(x-7) would have x-intercepts at -9 and 7 , and it would dip below the x-axis between these two values.

So the |...| flips that part above the x-axis, causing CUSPS at x =-9 and x=7

the derivative does not exist for those two values.
Hmm, DNE was incorrect.