A jump discontinuity occurs when the limits as x approaches a number from the left and right are not equal. Basically, the graph "jumps" from one number to another at that x value.
A point discontinuity occurs when limits as x approaches a number from the left and right are equal, but the actual value of f(x) at x is not equal to the limit. Basically, a point is missing and there is a "hole" in the graph at that x value.
Looking at your graph, you can see that at x=0, the graph "jumps" from a value of 2 as the graph approaches x=0 from the left to a value of 1 as the graph approaches x=0 from the right. That means there is a jump discontinuity at x=0.
You can also see that there is a "hole" in the graph at x=-2 and x=8 as seen by the open circle. There is no hole at x=3 because the circle is filled in. That means there is a point discontinuity at x=-2 and x=8.
Your answer is B) jump discontinuity at x=0; point discontinuities at x=-2 and x=8.
We have the following function: p (x) = - 2 (x-9) ^ 2 +200 We derive to find the maximum of the function: p '(x) = - 4 (x-9) Rewriting: p '(x) = - 4x + 36 We match zero: -4x + 36 = 0 We clear x x = 36/4 x = 9 degrees The maximum population occurs when x = 9. We evaluate the function for this value: p (9) = - 2 * (9-9) ^ 2 +200 p (9) = 200 Answer: The maximum number of fish is: p (9) = 200
