MA101 Study Guide - Final Guide: Intermediate Value Theorem, Mean Value Theorem, Squeeze Theorem
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Ma101 lab report 2 - ivt; mvt; squeeze theorem. Text reference: 3. 5. 1, 5. 1. 3, 3. 4: the intermediate value theorem (3. 5. 1) Intermediate value theorem (ivt): suppose f (x) is continuous on [a, b]. If f (a) < l < f (b) or f (b) < l < f (a), then there exists at least one c (a, b) such that f (c) = l. Note that the ivt doesn"t state the value(s) of c. if required, solve f (c) = l to nd c: the mean value theorem (5. 1. 3) Mean value theorem (mvt): if f (x) is continuous on [a, b] and di erentiable on (a, b), then there exists at least one c (a, b) such that: f (c) = f (b) f (a) Example: consider f (x) = x2 x2 + 2. Use the mvt to show there exists a c (0, 3) such that that f (c) =
there exists a value of 
such that 
at the interval 
.