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1. If f(x) = and g(x) = 3x, then g(f(2)) =
3. The slope of the line tangent to the graph of 3x2 + 5 ln y = 12 at (2, 1) is
4. The equation y = 2 - 3 sin (x - 1) has a fundamental period of
5. If , for all real numbers x, which of the following must be true?
I. f(x) is continuous everywhere.
II. f(x) is differentiable everywhere.
III. f(x) has a local minimum at x = 2.
6. For what value of x does the function f(x) = x3 - 9x2 - 120x + 6 have a local minimum?
7. The acceleration of a particle moving along the x-axis at time t is given by a(t) = 4t - 12. If the velocity is 10 when t = 0 and the position is 4 when t = 0, then the particle is changing direction at
8. The average value of the function f(x) = (x -1)2 on the interval from x = 1 to x = 5 is
10. If f(x) = (x2 + x + 11), then f′(0) =