If f(x) = x3 – 4x + p, and f(0) and f(1) are of opposite signs, then which of the following is necessarily true?
Explanation:
f(x) = x3 – 4x + p
∴ f(0) = p and f(1) = p – 3
p – 3 < p
As p and p – 3 are of opposite signs, p – 3 < 0 and p > 0.
∴ p < 3 and p > 0
∴ 0 < p < 3
Hence, option (b).
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