Please help solve, Thank you.Below is the graph of a polynomial function f with real coefficients. Use the graph to answer the following questions about f. All local extrema of f are shown in the graph. 8+6-4-2--6-2-9--8-(a) The function f is decreasing over which intervals? Choose all that apply.O (-00 , -9)O (-7, -3) O (-9, -3) O (1, 4)O (4, 7)O (7, 0 )(b) The function f has local maxima at which x-values? If there is more than one value,separate them with commas.(c) What is the sign of the leading coefficient of f?Select One(d) Which of the following is a possibility for the degree of f? Choose all that apply.O 4O 5O 6O 7O 8O 9 8-6-4-2--44.4-0,...(a) The function f is decreasing over which intervals? Choose all that apply.O (-00, -9)O (-7, -3) O (-9, -3) O (1, 4)O (4, 7)O (7, 0 )(b) The function f has local maxima at which x-values? If there is more than one value,separate them with commas.(c) What is the sign of the leading coefficient of f?Select OneSelect OnePositive(d)Negativesibility for the degree of f? Choose all that apply.Not enough informationO 6O 8O 9

Answered: 8- 6- 4- 2- -4 -4- -6- -8- (a) The…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Please help solve, Thank you.

Below is the graph of a polynomial function f with real coefficients. Use the graph to answer the following questions about f. All local extrema of f are shown in the graph.

8+
6-
4-
2-
-6
-2
-9-
-8-
(a) The function f is decreasing over which intervals? Choose all that apply.
O (-00 , -9)
O (-7, -3) O (-9, -3) O (1, 4)
O (4, 7)
O (7, 0 )
(b) The function f has local maxima at which x-values? If there is more than one value,
separate them with commas.
(c) What is the sign of the leading coefficient of f?
Select One
(d) Which of the following is a possibility for the degree of f? Choose all that apply.
O 4
O 5
O 6
O 7
O 8
O 9

8-
6-
4-
2-
-4
4.
4-
0,...
(a) The function f is decreasing over which intervals? Choose all that apply.
O (-00, -9)
O (-7, -3) O (-9, -3) O (1, 4)
O (4, 7)
O (7, 0 )
(b) The function f has local maxima at which x-values? If there is more than one value,
separate them with commas.
(c) What is the sign of the leading coefficient of f?
Select One
Select One
Positive
(d)
Negative
sibility for the degree of f? Choose all that apply.
Not enough information
O 6
O 8
O 9

Expert Solution

Step 1

Given that the graph of the polynomial.

(a) To find the function f is decreasing over which intervals:

From the graph, in the intervals, (-7,-3), (1,4), (7, $\infty$ ), the given function's graph rises downwards.

Thus, the function f is decreasing in (-7,-3), (1,4), (7, $\infty$ ).

(b)To find the function f has local maxima at which x-values:

From the graph, the function f attains its maximum at (-7,1), (1,0), (7,4).

Thus, the local maxima of the function f at x = -7, 1, 7.

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