The process of proving a root lies within a specific interval entails demonstrating that a function intersects the x-axis within that designated range. This is frequently accomplished by using the Intermediate Value Theorem. This theorem is applied to show that the function adopts values with contrasting signs at the interval's endpoints, thereby implying that it must intersect the x-axis somewhere within the interval.
| Topic | Problem | Solution |
|---|---|---|
| None | Prove that the function \(f(x) = x^2 - 4x + 4\) h… | Step 1: We first calculate the function values at the endpoints of the interval, i.e., \(f(1)\) and… |