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If function ƒ(x) = x3 + ax2 + bx + c is monotonically increasing ∀ x ∈ R, where a & b are prime numbers less than 10, then number of possible ordered pairs (a,b) is
Correct answer is '7'. Can you explain this answer?
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Verified Answer
If function ƒ(x) = x3+ ax2+ bx + c is monotonically increasing &f...
a, b ∈ {2, 3, 5, 7}
ƒ '(x) = 3x2 + 2ax + b ≥ 0 ∀ x ∈ R
D ≤ 0
4a2 – 12b ≤ 0
4(a2 – 3b) ≤ 0
a = 2 b = 2,3,5,7
a = 3 b = 3,5,7
a = 5 No solution
a = 7 No solution
Ordered pairs (a,b) are (2,2), (2,3), (2,5), (2,7), (3, 3), (3,5) & (3,7)
ƒ '(x) = 3x2 + 2ax + b ≥ 0 ∀ x ∈ R
D ≤ 0
4a2 – 12b ≤ 0
4(a2 – 3b) ≤ 0
a = 2 b = 2,3,5,7
a = 3 b = 3,5,7
a = 5 No solution
a = 7 No solution
Ordered pairs (a,b) are (2,2), (2,3), (2,5), (2,7), (3, 3), (3,5) & (3,7)
Most Upvoted Answer
If function ƒ(x) = x3+ ax2+ bx + c is monotonically increasing &f...
It is unclear what is being asked about the "If" function. The "If" function is a commonly used function in programming and spreadsheets that allows for conditional statements to be executed. It is typically used to perform different actions or calculations based on whether a certain condition is met.
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If function ƒ(x) = x3+ ax2+ bx + c is monotonically increasing ∀ x ∈ R, where a & b are prime numbers less than 10, then number of possible ordered pairs (a,b) isCorrect answer is '7'. Can you explain this answer?
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If function ƒ(x) = x3+ ax2+ bx + c is monotonically increasing ∀ x ∈ R, where a & b are prime numbers less than 10, then number of possible ordered pairs (a,b) isCorrect answer is '7'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If function ƒ(x) = x3+ ax2+ bx + c is monotonically increasing ∀ x ∈ R, where a & b are prime numbers less than 10, then number of possible ordered pairs (a,b) isCorrect answer is '7'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If function ƒ(x) = x3+ ax2+ bx + c is monotonically increasing ∀ x ∈ R, where a & b are prime numbers less than 10, then number of possible ordered pairs (a,b) isCorrect answer is '7'. Can you explain this answer?.
If function ƒ(x) = x3+ ax2+ bx + c is monotonically increasing ∀ x ∈ R, where a & b are prime numbers less than 10, then number of possible ordered pairs (a,b) isCorrect answer is '7'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If function ƒ(x) = x3+ ax2+ bx + c is monotonically increasing ∀ x ∈ R, where a & b are prime numbers less than 10, then number of possible ordered pairs (a,b) isCorrect answer is '7'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If function ƒ(x) = x3+ ax2+ bx + c is monotonically increasing ∀ x ∈ R, where a & b are prime numbers less than 10, then number of possible ordered pairs (a,b) isCorrect answer is '7'. Can you explain this answer?.
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