Let f(x) = x12 – x9 + x4 – x + 1. Which of the following is true ?

1.	Let f(x) = x12 – x9 + x4 – x + 1. Which of the following is true ? (A) f is one-one (B) f has a real root (C) f ′ never vanishes (D) f takes only positive values
Answer» Correct Option :- (D) f takes only positive values Explanation :- f(x) = x⁹ (x³ – 1) + x (x³ – 1) + 1 positive for x ≥ 1 or x ≤ 0 = 1 – x + x⁴ – x⁹ + x¹² positive for x∈(0, 1) f(x) is always positive

Let f(x) = x12 – x9 + x4 – x + 1. Which of the following is true ? (A) f is one-one (B) f has a real root (C) f ′ never vanishes (D) f takes only positive values

Answer»

Correct Option :- (D) f takes only positive values

Explanation :-

f(x) = x⁹ (x³ – 1) + x (x³ – 1) + 1 positive for x ≥ 1 or x ≤ 0

= 1 – x + x⁴ – x⁹ + x¹² positive for x∈(0, 1)

f(x) is always positive

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Let f(x) = x12 – x9 + x4 – x + 1. Which of the following is true ? (A) f is one-one (B) f has a real root (C) f ′ never vanishes (D) f takes only positive values

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