Practice Bounds in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

The upper and lower limits within which a quantity must lie; often expressed as a \leq x \leq b.

Temperature tomorrow will be between 60F and 75F. Those are bounds.

medium

For \(f(x) = -x^2 + 6x - 5\), find the maximum value (upper bound) on \([0, 5]\).

hard

Show that for all real \(x\), \(x^2 \geq 0\). What is the greatest lower bound (infimum) of \(x^2\)?

medium

For \(g(x) = 3x + 1\) on \([0, 4]\), find the minimum and maximum values.

hard

Prove that \(\sin(x) \leq 1\) and \(\sin(x) \geq -1\) for all \(x\) using the unit circle definition.