Intermediate value theorem
What Intermediate value theorem means in Mathematics A-Level, as defined for AQA, WJEC.
Definitions of Intermediate value theorem
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Reference: WJEC
If f(x) is continuous on a closed interval [a, b] and f(a) and f(b) have opposite signs, there exists at least one real root α ∈ (a, b) such that f(α) = 0.
If f is continuous on [a, b] and f(a) and f(b) have opposite signs, then there is at least one root between a and b.
Topics that use Intermediate value theorem
- I: Numerical methods (AQA A-Level)
- Numerical Methods (A2 Unit 3: Pure Mathematics B) (WJEC A-Level)
Related terms
- Trapezium rule
- Approximation and convergence
- Approximation and error
- bounds for the true integral
- cobweb diagram
- contextual problem solving
- divergence
- failure of sign change
Using Intermediate value theorem in the exam
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