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?
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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.
The maximum point is at the point where the gradient of the function is zero, represented by the first derivative.
0 = -6x-18
The maximum point is at the point where x=3
To obtain the maximum value, we substitute x=3 to the function:-
The functions maximum value is -106
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