Rolle Theorem - AP Calculus - Lecture Notes, Study notes of Calculus

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1/3 Calculus Section 3.2 Notes Learning Targets... 1. Use Rolle’s Theorem to find x-values in an interval 2. Use Mean Value Theorem (MVT) to find x-values in an interval LT: Use Rolle’s Theorem to find x-values in an interval e If... © fis Gontinuous on fa,b] & differentiable on (a,b) &... o f(a)= f(b) ® Then there is at least onec in (a,b) such that f fc) =0 ; Relative Relative maximum maximum i a c b \ a e b Fs (b) f is continuous on [a, 5]. FIGURE 3.8 (a) f is continuous on [a, b] and differentiable on (a, b). e Why doesn’t Rolle’s apply to the second figure? Identify the value(s) of c found by Rolle’s theorem. 1) Ii 0 | fl) =0 ot fi) f@ = 24 - 22 FIGURE 3.10 F'(x) = 0 for more than one x-value in the interval (—2, 2).