Question

Let f:R→R be defined as f(x) = |x⁴ – 1| + |x⁶ – 1|. Then find the total number of points at which f attains either a local maximum or local minimum.

Answer 1

We have f(x) = |x⁴ – 1| + |x⁶ – 1|

Clearly, the number of extremum is 5

at x = –1, – √(2/3), 0, √(2/3), 1