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1. If is replaced by u, then is equivalent to
2. The line tangent to the graph of function f at the point (8,1) intersects the y-axis at y = 3. Find f ′(8).
3. How many points of inflection does the function f have on the interval 0 ≤ x ≤ 6 if
The graph shows the rate at which tickets were sold at a movie theater during thelast hour before showtime. Using the right-rectangle method, estimate the size ofthe audience.
5. At what point of intersection of f (x) = 4sin x and g(x) = ln (x2) do their derivatives have the same sign?
6. Which statement is true?
The graph of f ′ is shown above. Which statements about f must be true for a < x < b ?
I. f is increasing.
II. f is continuous.
III. f is differentiable.
8. After a bomb explodes, pieces can be found scattered around the center of the blast.The density of bomb fragments lying x meters from ground zero is given by fragments per square meter. How many fragments will be found within 20 meters ofthe point where the bomb exploded?