Unformatted text preview: GROUP WORK 4, SECTION 3.3
Sparse Data Assume that f (x) and g (x) are differentiable functions about which we know very little. In fact, assume that all we know about these functions is the following table of data: l-l----ll This isn’t a lot of information. For example, we can’t compute f’ (3) with any degree of accuracy. But we
are still able to ﬁgure some things out, using the rules of differentiation. l. Leth (x) = (35% f(x). What is h’ (0)? 2. Let] (x) = —4f (x)g(x). What is j’ (1)? xf (x)
g (x) 3. Let k (x) = . What is k’ (—2)? 4. Let 1 (x) = x3 g (x). Ifl’ (2) = —48, what is g’ (2)? 5. Letm (x) = %. What is m’ (l)? ...
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