Find the exact instantaneous rate of change of h

Reference no: EM131006832

1. Suppose that f(x) and g(x) are differentiable functions and that the following information about them is known:

x	f(x)	f'(x)	g(x)	g'(x)
-1	2	-5	-3	4
2	-3	4	-1	2

If C(x) is a function given by the formula f(g(x)), determine C'(2). In addition, if D(x) is the function f(f(x)), find D'(-l).

2. Consider the basic functions f(x) = X³ and g(x) = sin(x).

a. Let h(x) = f(g(x)). Find the exact instantaneous rate of change of h at the point where x = π / 4.

b. Which function is changing most rapidly at x = 0.25: h(x) = f(g(x)) or r(x) = g(f(x))? Why?

c. Let h(x) = f(g(x)) and r(x) = g(f(x)). Which of these functions has a derivative that is periodic? Why?

3. Let functions p and q be the piecewise linear functions given by their respective graphs in Figure. Use the graphs to answer the following questions.

a. Let C(x) = p(q(x)). Determine C'(0) and C'(3).

b. Find a value of x for which C'(x) does not exist. Explain your thinking.

2286_The graphs of p in blue and q in green.png

Figure: The graphs of p (in blue) and q (in green).

Let Y(x) = q(q(x)) and Z(x) = q(p(x)). Determine Y'(-2) and Z'(0).

Reference no: EM131006832

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