Proofs involving inequalities (HSC SSCE Mathematics Extension 2): Quizzes
📚Quizzes
Practise the questions
10 questions from this quiz
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Practise the questions
10 questions from this quiz
What does the AM-GM Inequality imply about means?
What does the AM-GM Inequality imply about means?
AM is less than or equal to GM
What happens when multiplying by a negative?
What happens when multiplying by a negative?
Inequality direction reverses
What is proof by contradiction?
What is proof by contradiction?
Assuming the negation leads to a contradiction
What does the Cauchy-Schwarz Inequality state?
What does the Cauchy-Schwarz Inequality state?
Sum of products ≤ product of sums
What is the first step in proving inequalities?
What is the first step in proving inequalities?
Apply algebraic manipulation
What does the AM-GM inequality imply for non-negative a and b?
What does the AM-GM inequality imply for non-negative a and b?
a + b ≥ 2√ab
What can be concluded from the inequality x^2 + 1 < 0?
What can be concluded from the inequality x^2 + 1 < 0?
No real solutions exist
What is the outcome of adding a positive constant?
What is the outcome of adding a positive constant?
Inequality direction remains the same
What is the minimum of x^2 + y^2 - 2xy?
What is the minimum of x^2 + y^2 - 2xy?
0
What is the role of derivatives in inequalities?
What is the role of derivatives in inequalities?
To find critical points