The table below represents values of differentiable functions, f and g, and their first derivatives. Use the table of values to answer the questions that follow. f(x) f'(x) g(x) g'(x) -3 -4 -2 -2 1 -2 5 2 -3 2 -4 2 -4 -6 A. Is there a value of r on –3 < r < 2 such that f (r) = 0 ? Give a reason for your answer. 3. 3. 3.
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The table below represents values of differentiable functions, f and g, and their first derivatives.
Use the table of values to answer the questions that follow.
f(x)
f'(x)
g(x)
g'(x)
-3
8
-4
-2
-2
2
1
-2
2
-3
2
-4
2
-4
-6
A. Is there a value of r on -3 < r < 2 such that f (r) = 0 ? Give a reason for your answer.
B. Approximate the value of g"(1.5). What does this value say about the graph of g when x = 1.5?
C. If h(x) = [f (x)]² + g(x), what is the equation of the line tangent to the graph of h at x = -2?
D. Is there guaranteed to exist a value of x = c on –2 < c < 2, such that h' (c) = 0? Give a reason for
your answer.
3.
3.
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