Answer the questions below about the quadratic function.
g(x)= -x^2 -2x +1
a.) does the function have a minimum or maximum value? (answer would be just min or max)
b.) where does the minimum or maximum value occur?
c.) what is the functions minimum or maximum value?
Thank you for the opportunity to help you with your question!
to determine whether the function has a maximum or minimum point we differentiate it twice
Hence g'(x) =-2x-2
and g"(x) =-2
Therefore the function has a maximum point since sign of the second derivative is negative.
The maximum point occurs at the point where the slope of the function is zero(0); derived from the first derivative.
0 = -2x-2
Therefore the maximum point occurs at the value of the function where x =1.
Substituting x=1 into the function gives:-
g(x) = (-1)^2-2(1)+1 = -2
Therefore the functions maximum point is (1,-2) and maximum value is -2
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