Answer :
The descriptions of the quadratic functions f(x) and g(x) are as follows:
f(x) = [tex]-2x^{2} +9[/tex]
x g(x)
0 −5
1 3
2 11
3 3
4 −5
Which sentence compares the two functions' maximum values the most effectively?
(a)The maximum value is the same for both functions.
(b) f(x) has a greater maximum value than g(x).
(c) The greatest value of g(x) is bigger than that of f(x).
(d) The maximum values cannot be determined.
The statement that best compares the maximum value of the two functions is g(x) has a greater maximum value than f(x) that is Option (c).
The maximum value is the point at which a function reaches its peak is known as its maximum value.
To compare both functions.
Take function f(x)= [tex]-2x^{2} +9[/tex]
Differentiate the function f(x)
f'(x) = -4x
Take f'(x) as 0
-4x = 0
x = 0
Substitute x = 0 in f(x)
f(0) = [tex]-2(0)^{2} +9[/tex]
f(0) = 9
This means that the greater value of function f(x) is 9.
From the table of function g(x), the maximum is 11.
11 is greater than 9
Therefore, The greater value of g(x) is bigger than that of f(x).
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