Question

The set of values of p for which the points of extremum of the function f(x) = x³ – 3px² + 3(p² – 1)x + 1 lie in the interval (–2, 4), is ______.

Options

• (–3, 5)

• (–3, 3)

• (–1, 3)

• (–1, 5)

Answer 1

The set of values of p for which the points of extremum of the function f(x) = x³ – 3px² + 3(p² – 1)x + 1 lie in the interval (–2, 4), is (–1, 3).

Explanation:

f '(x) = 0

⇒ x = p – 1, p + 1

∴ –2 < p – 1, and p + 1 < 4

p ∈ R

⇒ p > –1 and p < 3

p ∈ (–1, 3)