What lies beneath the accumulation function?

Accumulation

Sketch the graph ƒ(t) = t and complete the table of values for the function A(x).

x 0 1 2 3 4

x 0 -1 -2 -3 -4

The Second Fundamental Theorem of Calculus

If ƒ is a continuous function on some interval [a, b] and an accumulation

function A is defined by then

Let's look at this geometrically ...

Given each accumulation function A(x), find it's derivative A'(x).

Accumulation functions are COMPOSITE FUNCTIONS!

Given each accumulation function find it's derivative.