Let \(H(x)\) be a quadratic function with \(H'(x) = 5x - 10\).

\(H'(x) = 0\) at \(t = \answer {2}\).

\(H'(x) < 0\) on \(\left ( \answer {-\infty }, \answer {2} \right )\).

\(H'(x) > 0\) on \(\left ( \answer {2}, \answer {\infty } \right )\).

\(H(x)\) decreases on \(\left ( \answer {-\infty }, \answer {2} \right )\).

\(H(x)\) increases on \(\left ( \answer {2}, \answer {\infty } \right )\).

The minimum of \(H(x)\) is located at \(x = \answer {2}\).

2025-05-18 05:16:36