Mathematics - Application of Derivative Question with Solution | TestHub

For all x near 0 with x != 0 and |x| < 1, f(x) = |x| < 1, while f(0) = 1. So f(0) >= f(x) for every x in a neighbourhood of 0, which means f has a local maximum at x = 0 (the point (0,1) sits above the V-shaped graph of y = |x|). Answer: option A.