Question

If a, b, c are real numbers, find the intervals in which f(x) = |(x + a², ab, ac), (ab, x + b², bc), (ac, bc, x + c²)| is increasing or decreasing.

Answer 1

We have

= (x + a² + b² + c²)x²

⇒ f(x) = (x + a² + b² + c²)x²

⇒ f'(x) = 2(x + a² + b² + c²)x + x²

⇒ f'(x) = x {3x + 2(a² + b² + c²)}

Now, f'(x) = 0 gives

⇒ x{3x + 2(a² + b² + c²)} = 0

⇒ x = 0, – 2(a² + b² + c²)/3

Thus, f(x) increasing in