4. Use the steps from class to sketch the graphs of the following functions. (a) f(x) = x² - 2x²+3 (b) f(x) = 1 x²-9 (c) f(x) = x5/3-5x2/3 5. A given function satisfies the following conditions: i. f(-4) = 0, f(0) = -3, f(1) = 0, f(2) = 2, f(3) = 1, and f(4) = 0; ii. f'(x)>0 on (0,2); iii. f'(x) <0 on (-00, 0) and (2, 0); iv. f"(x)>0 on (-00, 1) and (3, 0); and v. f"(x) <0 on (1, 3). (a) On what intervals is the graph of f increasing? Decreasing? (b) At what point(s) (if any) does f have a relative maximum? Relative minimum? (c) On what intervals is the graph of ƒ concave upward? Downward? (d) At what point(s) (if any) does f have inflection points? (e) Sketch a graph of f. 6. Find the absolute maximum and absolute minimum values of f on the given interval. (a) f(x) = 2x³-3x² - 12x+1, [-2,3] (b) f(x) = (x²-1)³, [−1, 2]
4. Use the steps from class to sketch the graphs of the following functions. (a) f(x) = x² - 2x²+3 (b) f(x) = 1 x²-9 (c) f(x) = x5/3-5x2/3 5. A given function satisfies the following conditions: i. f(-4) = 0, f(0) = -3, f(1) = 0, f(2) = 2, f(3) = 1, and f(4) = 0; ii. f'(x)>0 on (0,2); iii. f'(x) <0 on (-00, 0) and (2, 0); iv. f"(x)>0 on (-00, 1) and (3, 0); and v. f"(x) <0 on (1, 3). (a) On what intervals is the graph of f increasing? Decreasing? (b) At what point(s) (if any) does f have a relative maximum? Relative minimum? (c) On what intervals is the graph of ƒ concave upward? Downward? (d) At what point(s) (if any) does f have inflection points? (e) Sketch a graph of f. 6. Find the absolute maximum and absolute minimum values of f on the given interval. (a) f(x) = 2x³-3x² - 12x+1, [-2,3] (b) f(x) = (x²-1)³, [−1, 2]
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter8: Linear Functions
Section8.7: Function Notation
Problem 17E
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exam review please help!
![4. Use the steps from class to sketch the graphs of the following functions.
(a) f(x) = x² - 2x²+3
(b) f(x) =
1
x²-9
(c) f(x) = x5/3-5x2/3
5. A given function satisfies the following conditions:
i. f(-4) = 0, f(0) = -3, f(1) = 0, f(2) = 2, f(3) = 1, and f(4) = 0;
ii. f'(x)>0 on (0,2);
iii. f'(x) <0 on (-00, 0) and (2, 0);
iv. f"(x)>0 on (-00, 1) and (3, 0); and
v. f"(x) <0 on (1, 3).
(a) On what intervals is the graph of f increasing? Decreasing?
(b) At what point(s) (if any) does f have a relative maximum? Relative minimum?
(c) On what intervals is the graph of ƒ concave upward? Downward?
(d) At what point(s) (if any) does f have inflection points?
(e) Sketch a graph of f.
6. Find the absolute maximum and absolute minimum values of f on the given interval.
(a) f(x) = 2x³-3x² - 12x+1, [-2,3]
(b) f(x) = (x²-1)³, [−1, 2]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0358b5fa-6a35-4918-bb57-f6ae9ca4088e%2F5ebd4f9c-d201-46ab-9014-ddfc8048c4d4%2Fny8hvv4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4. Use the steps from class to sketch the graphs of the following functions.
(a) f(x) = x² - 2x²+3
(b) f(x) =
1
x²-9
(c) f(x) = x5/3-5x2/3
5. A given function satisfies the following conditions:
i. f(-4) = 0, f(0) = -3, f(1) = 0, f(2) = 2, f(3) = 1, and f(4) = 0;
ii. f'(x)>0 on (0,2);
iii. f'(x) <0 on (-00, 0) and (2, 0);
iv. f"(x)>0 on (-00, 1) and (3, 0); and
v. f"(x) <0 on (1, 3).
(a) On what intervals is the graph of f increasing? Decreasing?
(b) At what point(s) (if any) does f have a relative maximum? Relative minimum?
(c) On what intervals is the graph of ƒ concave upward? Downward?
(d) At what point(s) (if any) does f have inflection points?
(e) Sketch a graph of f.
6. Find the absolute maximum and absolute minimum values of f on the given interval.
(a) f(x) = 2x³-3x² - 12x+1, [-2,3]
(b) f(x) = (x²-1)³, [−1, 2]
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