Question

If m is the number of points of extremum of f(x) = |x| + |x³ – 1| and n is the least value of g(x) = 1/(|x – 2| + 1) + |x – 3|, find the value of (m + 2n + 2).

Answer 1

We have f(x) = |x| + |x³ – 1|

Thus, the number of points of extremum is 3

Thus, the minimum value of g (x) is 1/2 at x = 3.

So, n = 1/2

Hence, the value of (m + 2n + 2) = 3 + 1 + 2 = 6.