F09Graphsample1ANS

F09Graphsample1ANS - The following is a graph of the first derivative f(x of a function y = f(x You may assume f(x is defined for all real numbers

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
The following is a graph of the first derivative f’(x) of a function y = f(x). You may assume f(x) is defined for all real numbers. y Use this graph of f’(x) to answer the 2 y = f’(x) following questions about the graph of f(x). 1 -7-6-5-4-3–2-1 1 2 3 4 5 6 7 8 x -2 a. On what interval(s) is the graph of f(x) concave up? ANSWER : The graph of f(x) is concave up on the intervals in which f’’(x) > 0, ie on the intervals in which f’(x) is increasing, that is (- , -1) and (4,+ ). b. On what interval(s) is the graph of f(x) concave down? ANSWER: The graph of f(x) is concave down on the intervals in which f’’(x) < 0, ie on the intervals in which f’(x) is decreasing, that is (-1,4). c. Give the x coordinate of the point(s) of inflection. ANSWER: The points of inflection are the points about which the graph changes concavity. These may be the points at which f’’(x) DNE or at which f’’(x) = 0. The x coordinates for the points of inflection for the graph of y = f(x) are x = -1 and x = -4. (In this example
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 09/25/2011 for the course CALCULUS 135 taught by Professor Augustarainsford during the Spring '11 term at Rutgers.

Ask a homework question - tutors are online