The average value of y=v(x) equals 4 for 1≤x≤6, and equals 5 for 6≤x≤8. what is the average value of v(x) for 1≤x≤8 ?
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Answer:
The value of a will be
Step-by-step explanation:
Start by graphing the parabola and the three points of the triangle. These points are at intersections of y=a(x-1)(x-4) and the axes
so the y = 0 points are (1,0) and (4,0).
The x = 0 intersection is when y=a(-1)(-4) or (0,4a)
The base and height of this triangle are
The base would be the distance between the y=0 intersections and the height would be the y value of the other vertex.
Hence, base=3 units and height = 4a units. Thus, area can be calculated as
∵ the parabola opens downward therefore a will be negative.
hence,