• If you are asked to find z- or yvalues, enter either a number or a list of numbers separated by commas. If there are no solutions, enter None. If you are asked to find an interval or union of intervals, use interval notation. Enter () if an interval is empty. • If you are asked to find a limit, enter either a number, I for 0o, 1 for -00, or DNE if the limit does not exist. ) Calculate the first derivative of f. Find the critical numbers of f. where it is increasing and decreasing, and its local extrema. "(e) =O ritical numbers z= nion of the intervals where f(z) is increasing nion of the intervals where f(z) is decreasing ocal maxima z ocal minima z ) Find the following left- and right-hand limits at the vertical asymptote z=-3. lim lim ind the following left- and right-hand limits at the vertical asymptote z = 3. 6z lim lim ind the following limits at infinity to determine any horizontal asymptotes. 6z lim lim ) Calculate the second derivative of f. Find where f is concave up, concave down, and has inflection points. "(-) =O nion of the intervals where f(z) is concave up nion of the intervals where f(z) is concave down flection points z= ) The function f is ? v for all z in the domain of f. and therefore its graph is symmetric about the ? because ? ) Answer the following questions about the function f and its graph. he domain of f is the set (in interval notation) he range of f is the set (in interval notation) -intercept -intercents
• If you are asked to find z- or yvalues, enter either a number or a list of numbers separated by commas. If there are no solutions, enter None. If you are asked to find an interval or union of intervals, use interval notation. Enter () if an interval is empty. • If you are asked to find a limit, enter either a number, I for 0o, 1 for -00, or DNE if the limit does not exist. ) Calculate the first derivative of f. Find the critical numbers of f. where it is increasing and decreasing, and its local extrema. "(e) =O ritical numbers z= nion of the intervals where f(z) is increasing nion of the intervals where f(z) is decreasing ocal maxima z ocal minima z ) Find the following left- and right-hand limits at the vertical asymptote z=-3. lim lim ind the following left- and right-hand limits at the vertical asymptote z = 3. 6z lim lim ind the following limits at infinity to determine any horizontal asymptotes. 6z lim lim ) Calculate the second derivative of f. Find where f is concave up, concave down, and has inflection points. "(-) =O nion of the intervals where f(z) is concave up nion of the intervals where f(z) is concave down flection points z= ) The function f is ? v for all z in the domain of f. and therefore its graph is symmetric about the ? because ? ) Answer the following questions about the function f and its graph. he domain of f is the set (in interval notation) he range of f is the set (in interval notation) -intercept -intercents
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
ChapterP: Prerequisites
SectionP.6: Analyzing Graphs Of Functions
Problem 4ECP
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