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Accumulation Function

Accumulation Function. Prepare to take notes. The powerpoint is on the web page. Consider the graph f(t) = 2. What is the value of ?.

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Accumulation Function

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  1. Accumulation Function Prepare to take notes. The powerpoint is on the web page

  2. Consider the graph f(t) = 2

  3. What is the value of ?

  4. Example 1: Think of f(x) as the rate of snowfall over a period of time. For instance, at x = 1, snow is falling at 3 inches per hour, at x = 3, it is not snowing, and at x = 4, snow is melting at 4 inches per hour.

  5. Now let’s consider If we take the d/dx of an integral, what would you expect to happen? So is the same thing as

  6. So is the same thing as

  7. On what subintervals of [0, 8] is F(x) increasing? Decreasing? Where in the interval [0, 8] doe F(x) have abs min and max? What are those values? Find the concavity of F(x) and any inflection points. Justify your answer. Sketch the graph of F(x)

  8. Example 2: Let where f is the graph below. Find the following: a) F(0)= b) F(2)= c) F(4)= d) F(6) = e) F(-1) = f) F(-2) = g) F(-3) = h) F(-4) = i) F’(4) = j) F’(2) = k) F’(6) = l) F’(-3) =

  9. m) On what intervals is F increasing and decreasing, Justify. n) Find the minimum and its value. o) Find the maximum and its value. p) Find the concavity and justify your answer. q) Find any points of inflection. r) Sketch the function F

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