Consider the function f(t) = t² - 5t + 4 and the area function

a. Graph f 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 f.

d. Give a geometrical 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 f and the t-axis on the interval [0, t₁] equals the area bounded by the graph of f and the t-axis on the interval [t₁, b].

g. If f is an integrable function andis it always true that the local extrema of A occur at the zeros of f ? Explain.

Transcribed Image Text:

= S¨f(1) dt. A(x) A(x) = ["f(t) dt.