Answer:
(-2.4, 37.014)
Step-by-step explanation:
We are not told how to approach this problem.
One way would be to graph f(x) = x^5 − 10x^3 + 9x on [-3,3] and then to estimate the max and min of this function on this interval visually. A good graph done on a graphing calculator would be sufficient info for this estimation. My graph, on my TI83 calculator, shows that the relative minimum value of f(x) on this interval is between x=2 and x=3 and is approx. -37; the relative maximum value is between x= -3 and x = -2 and is approx. +37.
Thus, we choose Answer A as closest approx. values of the min and max points on [-3,3]. In Answer A, the max is at (-2.4, 37.014) and the min at (2.4, -37.014.
Optional: Another approach would be to use calculus: we'd differentiate f(x) = x^5 − 10x^3 + 9x, set the resulting derivative = to 0 and solve the resulting equation for x. There would be four x-values, which we'd call "critical values."
The answer would be B) -5, 3. The roots can be found where the graph crosses the x-axis, which on this graph is -5 and 3.
You want to find the volume inside the hemisphere 
(i.e. inside the sphere but above the plane 
) and outside the cylinder 
. Call this region 
.
In cylindrical coordinates, we have
(where 
)
You line up the numbers shown in the photo, then add each column
