Consider the function f(t) = t 2 - 5t + 4 and the area function a. Graph

Question:

Consider the function f(t) = t2 - 5t + 4 and the area function= S¨f(1) dt. A(x)

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 xand 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 andA(x) = [is it always true that the local extrema of A occur at the zeros of f ? Explain.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For  book-img-for-question

Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

Question Posted: