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A curve has equation $y = f(x)$ The curve has a point of inflection at $x = 7$ It is given that $f'(7) = a$ and $f''(7) = b$, where $a$ and $b$ are real numbers - AQA - A-Level Maths Mechanics - Question 2 - 2021 - Paper 2
Question 2
A curve has equation $y = f(x)$ The curve has a point of inflection at $x = 7$ It is given that $f'(7) = a$ and $f''(7) = b$, where $a$ and $b$ are real numbers. Ide... show full transcript
Worked Solution & Example Answer:A curve has equation $y = f(x)$ The curve has a point of inflection at $x = 7$ It is given that $f'(7) = a$ and $f''(7) = b$, where $a$ and $b$ are real numbers - AQA - A-Level Maths Mechanics - Question 2 - 2021 - Paper 2
Step 1
Identify which one of the statements below must be true.
Answer
To determine whether must equal zero, we analyze the information given:
A point of inflection is where the concavity of a function changes, which implies that the second derivative at that point, , must equal zero. However, there is no direct requirement for the first derivative at that point, , leading to four possibilities:
- It could be zero,
- It could be positive,
- It could be negative, or
- It could be undefined.
Given that no specific condition is stated for other than what is necessary for a point of inflection, we conclude that:
Therefore, the correct answer must be: