Q352 · Practice questionTechnology-freeComplex familiar5 marks
QUESTION 352 (5 marks)
Let .
a)[2 marks]
Determine .
b)[2 marks]
Determine in simplest form.
c)[1 mark]
Determine .
WORKED SOLUTION
5 marksPractice marking scheme
ANSWER
a) . b) . c) .
Worked solution
a) Apply the product and chain rules to both factors.
b) Differentiate the result: , then collect terms.
c) Substitute into the second derivative.
Exact answers unless rounding is specified; equivalent forms accepted. Retain unrounded intermediate values.
Uses the product rule.
Obtains the first derivative with both chain factors.
Differentiates both terms of the first derivative.
Simplifies the second derivative.
Evaluates the second derivative at zero.
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