Description
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?
Explanation & Answer
Thank you for the opportunity to help you with your question!
g(x)= -x^2 -2x +1
a.
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.
b.
The maximum point occurs at the point where the slope of the function is zero(0); derived from the first derivative.
0 = -2x-2
2x=2
x=1
Therefore the maximum point occurs at the value of the function where x =1.
c.
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
Please let me know if you need any clarification. I'm always happy to answer your questions.
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