Q353 · Practice questionTechnology-freeComplex familiar5 marks
QUESTION 353 (5 marks)
Consider for .
a)[2 marks]
Determine in factorised form.
b)[3 marks]
Determine and classify the stationary point. Justify whether it is a global extremum.
WORKED SOLUTION
5 marksPractice marking scheme
ANSWER
a) . b) is the global minimum.
Worked solution
a) The quotient rule gives .
b) All factors other than are positive on the domain. Hence the derivative is negative for and positive for . The unique stationary point is the global minimum.
Exact answers unless rounding is specified; equivalent forms accepted. Retain unrounded intermediate values.
Uses the quotient rule correctly.
Obtains the factorised first derivative.
Determines x=-1.
Determines the y-coordinate.
Justifies a global minimum using derivative signs on the full domain.
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