Increasing and decreasing functions
Answers are for parents and teachers.
1
Compare 6^(−1/2) and 9^(−1/2).
6^(−1/2) > 9^(−1/2), because r < 0 and 6 < 9
2
Solve x^(2/3) = 9 (x > 0).
27
3
Find the positive root of x⁻² = 1/16.
4
4
Which of y = x^(1/4), y = x^(−1/4), y = x⁵ decrease for x > 0?
only y = x^(−1/4)
5
Prove that y = x − 1/x increases for x > 0.
For x₁ > x₂ > 0: y(x₁) − y(x₂) = (x₁ − x₂) + (x₁ − x₂)/(x₁x₂) = (x₁ − x₂)(1 + 1/(x₁x₂)) > 0.