Question

If the function f(x) = |x²+ a |x| + b| has exactly three points of non-differentiability, then which of the following may hold

• A. b = 0, a < 0
• B. b < 0, a Î R
• C. b > 0, a Î R
• D. b < 0, a Î R^–

Answer 1

Answer: (A)

b = 0, a < 0

Answer 2

b = 0 , a < 0

f(x) = x² + ax + b is quadratic polynomial cut x axis at x = 0 and x = – a

f(x) = x² + ax + b

f (| x |) = x² + a |x| + b

| f|x| = | x² + a |x| + b|

Exactly at three points function is not differentiable.