Question

The function \[ f(x)=x|x-1|+|x+2| \] is

• A. Increasing in \((-\infty,-2)\cup(1,\infty)\) and decreasing in \((-2,1)\)
• B. Decreasing in \((-\infty,-2)\cup(1,\infty)\) and increasing in \((-2,1)\)
• C. Monotonically decreasing on \(\mathbb{R}\)
• D. Monotonically increasing on \(\mathbb{R}\)

Hint:

For absolute value functions, always locate the critical points where the expressions inside the modulus become zero. Break the real line into intervals and simplify the function separately on each interval.

Answer 1

The Correct Option is D