LMVT application: proving inequalities and existence ([f(b)−f(a)]/(b−a) = f'(c) for some c in (a,b) → use bounds on f' to)
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[f(b)−f(a)]/(b−a) = f'(c) for some c in (a,b) → use bounds on f' to bound f(b)−f(a)
What each symbol means
| Symbol | What it stands for |
|---|---|
| c | Point guaranteed by LMVT in (a,b) |
| f | Function continuous on [a,b], differentiable on (a,b) |
When to use this
f continuous on [a,b] and differentiable on (a,b). Application: if m ≤ f'(x) ≤ M on (a,b), then m(b−a) ≤ f(b)−f(a) ≤ M(b−a).