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Material Type: Quiz; Professor: Null; Class: Calculus I; Subject: Mathematics; University: The University of Tennessee-Martin; Term: Fall 2009;
Typology: Quizzes
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(1.) For what values does the graph of 푓 (푥) = 푥^3 + 3푥^2 + 푥 + 3 have a horizontal tangent?
(2.) Let 푓 (푥) = 2 − 푥 for 푥 ≤ 1 and 푓 (푥) = 푥^2 − 2 푥 + 2 for 푥 > 1. Is 푓 differentiable at 푥 = 1? Sketch the graphs of 푓 and 푓 ′.
(3.) Let 푓 (푥) be defined to be 푥^2 for 푥 ≤ 2 and 푚푥 + 푏 if 푥 > 2. Find the values of 푚 and 푏 that make 푓 differentiable everywhere.
