Brainlag PlusIf f(a) and f(b) have different signs, a continuous graph must cross the axis between them. Narrow the interval to find a root.
The sign changes, so it crosses
f(x) = x³ + 2x − 7. f(1) = −4 (below the axis) and f(2) = 5 (above).
The graph is unbroken, so it crosses the x-axis between 1 and 2: f(x) = 0 has a root there.
- f(1.6) = −0.70 and f(1.7) = 0.31
- so the root is between 1.6 and 1.7
- f(1.65) = −0.21, negative
- so the root is between 1.65 and 1.7: it is 1.7 to 1 d.p.
The rest of this lesson and its 7 practice questions are in Plus.
Screen 1 of 3, free to read.
- 7 exam-style questions, marked as you go, each with a worked solution
- The Graphing Calculator beside every question
- Anything you get wrong is saved to your flashcards