Intermediate Value - AP Calculus - Lecture Notes, Study notes of Calculus

Download Intermediate Value - AP Calculus - Lecture Notes and more Study notes Calculus in PDF only on Docsity!

Calculus Section 1.4B Learning Targets... 1. Use Intermediate Value Theorem (IVT) to analyze function behavior in an interval LT: Use Intermediate Value Theorem (IVT) to analyze function behavior in an interval If fis continuous on the closed interval [a,b], and k is any number between f(a) & f(b), then there is at least one c in [a,b] such that f(c) =k e Need to prove continuity on the interval before using IVT ¢ Translation: Because it’s continuous, the curve must hit all function values between the endpoints Explain why the function has a zero on the interval. Find the value of c. 1) f(x) =x? — 4x + 3, [2,4] Priynomial Funck ion Continues ener trare €Qy= -t Ruy = 3 FQayecosd FOp ee i a) ve thete is @ ere on TE) buy IVT O=z\y 4x 43 O= Cx-190Cx- 3) yeu ¥23 & not 10 c= Cry 1/1