Calc 1 one Two Questions HW

Written Homework 1, Math122B section 5.

SHOW ALL WORK/ REASONINGS AND USE PROPER NOTATION FOR

FULL CREDIT.

1 Using the following graph, compute:

a) h′(2) if h(x) = (f(x))3

b) k′(2) if k(x) = 3f(x)

c) g′(2) if g(x) = (f(x))−1

d) m′(5) if m(x) = f−1(x)

Figure 1: Figure for problem 1.

2 If k ≥ 1, the graphs of y = sin x and y = ke−x intersect for x ≥ 0. Find the smallest value of k for which the graphs are tangent. What are the coordinates of the point of tangency?

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