The continuous function f f is defined for 4x4 4 x 4 . The
Question:
The continuous function f f is defined for −4≤x≤4 − 4 ≤ x ≤ 4 . The graph of f f , shown above, consists of two line segments and portions of three parabolas. The graph has horizontal tangents at x=−12, x=12 x = − 1 2 , x = 1 2 and x=52 x = 5 2 . It is known that f(x)=−x2+5x−4 f ( x ) = − x 2 + 5 x − 4 for 1≤x≤4 1 ≤ x ≤ 4 . The areas of regions A and B bounded by the graph of f f and the x− x − axis are 3 and 5, respectively. Let g g be the function defined by g(x)=∫x−4f(t)dt g ( x ) = ∫ − 4 x f ( t ) d t .
(a) Find g(0) and g(4).
(b) Find the absolute minimum value of g on the closed interval [-4,4]. Justify your answer.
(c) Find all interval for which the graph of g is concave down. Give a reason for your answer.
College Algebra Graphs and Models
ISBN: 978-0321845405
5th edition
Authors: Marvin L. Bittinger, Judith A. Beecher, David J. Ellenbogen, Judith A. Penna