Description
g(x)= -3x^2 - 18x - 25
a.) Does the funtion have a maximum or minimum value?
b.) Where does the minimum or maximum value occur?
c.) What is the functions minimum or maximum value?
Explanation & Answer
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g(x)= -3x^2 - 18x - 25
a.
To determine whether the function has a minimum or maximum point, we differentiate the function twice.
Therefore, g'(x) = -6x-18
g"(x) = -6
The function has a maximum point since the second derivative is negative.
b.
The maximum point is at the point where the gradient of the function is zero, represented by the first derivative.
0 = -6x-18
6x=18
x= 3
The maximum point is at the point where x=3
c.
To obtain the maximum value, we substitute x=3 to the function:-
g(x) =-3(3^2)-18(3)-25
=-27-54-25
= -106
The functions maximum value is -106
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