Q354 · Practice questionTechnology-freeComplex familiar3 marks
QUESTION 354 (3 marks)
A student claims that the graph of has a point of inflection at because . Evaluate the reasonableness of the claim.
a)[3 marks]
Use calculus and explain your reasoning.
WORKED SOLUTION
3 marksPractice marking scheme
ANSWER
The claim is false: is positive on both sides of zero, so concavity does not change.
Worked solution
and . Although the second derivative is zero at , it does not change sign there. The graph is concave up on both sides, so is not a point of inflection.
Exact answers unless rounding is specified; equivalent forms accepted. Retain unrounded intermediate values.
Determines the second derivative.
Checks its sign on both sides of zero.
Rejects the claim because concavity does not change.
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