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A(x) = Säf(1) dt A(x) = [f(t) dt

- November 14, 2022 - Edwin Tunner

Consider the function
ƒ(t) = t2 – 5t + 4 and the area function shown
a. Graph ƒ on the interval [0, 6].
b. Compute and graph A on the interval [0, 6].
c. Show that the local extrema of A occur at the zeros of ƒ.
d. Give a geometric and analytical explanation for the observation
in part (c).
e. Find the approximate zeros of A, other than 0, and call them x1
and x2, where x1 < x2.
f. Find b such that the area bounded by the graph of ƒ and the
t-axis on the interval [0, x1] equals the area bounded by the
graph of ƒ and the t-axis on the interval [x1, b].
g. If ƒ is an integrable function and function given (257), is it
always true that the local extrema of A occur at the zeros of ƒ?
Explain.

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