Let A, B, and C represent the areas contained by te curve and the x-axis such that area A equals area B and both A and B are greater than area C. We will review many important concepts, approaching from many different directions.
http://tinypic.com/r/klpna/5
^Theres the picture of the graph
I already did A-E, but i need help with F
f) If f(0) = 4, estimate f(8)
http://tinypic.com/r/klpna/5
^Theres the picture of the graph
I already did A-E, but i need help with F
f) If f(0) = 4, estimate f(8)
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Because f(t) = ∫df/dt dt, and because the areas of A and B are equal, f(6) = f(0) = 4. So we have to find out what happens to f(t) between t=6 and t=8.
The average slope of the function over the interval (6, 7) seems to be -5/4, so we think f(7) = f(6) - 5/4 = 4 - 5/4 = 11/4. The average slope over the interval (7, 8) seems to be -3/2, so f(8) = f(7) - 3/2 = 11/4 - 3/2 = (11 - 6)/4 = 5/4. (Answer)
The average slope of the function over the interval (6, 7) seems to be -5/4, so we think f(7) = f(6) - 5/4 = 4 - 5/4 = 11/4. The average slope over the interval (7, 8) seems to be -3/2, so f(8) = f(7) - 3/2 = 11/4 - 3/2 = (11 - 6)/4 = 5/4. (Answer)