MATA37H3 Study Guide - Midterm Guide: Product Rule, Maxima And Minima
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Please read the following statement and sign below: I understand that any breach of academic integrity is a violation of the code of behaviour on academic matters. By signing below, i pledge to abide by the code. Mata37h3 page 2 of 9 (1) suppose f and g are injective functions satisfying the following: 3 f (x) f(cid:48)(x) 1 10 f(cid:48)(cid:48)(x) 2. 1 (a) (5 points) determine (g f ) 1(2). (you must show your work to receive credit. ) First observe that (g f ) 1 = f 1 g 1, so (g f ) 1(2) = f 1(cid:16) (cid:17) f (1) = 2, we have f 1(2) = 1. Since g is injective and g(2) = 2, we see that g 1(2) = 2. = 10, what is g(cid:48)(2)? (you must show your work to receive (cid:18) g(x) x d dx (b) (5 points) if credit. ) We have (cid:19)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)x=2 (cid:18) g(x) d dx x (cid:19) g(cid:48)(x)x g(x) x2.
