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A curve has equation $y = f(x)$ The curve has a point of inflection at $x = 7$ - AQA - A-Level Maths Pure - 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. Id... show full transcript
Worked Solution & Example Answer:A curve has equation $y = f(x)$ The curve has a point of inflection at $x = 7$ - AQA - A-Level Maths Pure - Question 2 - 2021 - Paper 2
Step 1
Identify which one of the statements below must be true.
Answer
At a point of inflection, the second derivative of a function changes its sign, which indicates that the curvature of the function is changing. Therefore, it is necessary for the second derivative at that point to be zero, indicating that it is a potential point of inflection.
In this case, since it is given that there is a point of inflection at , we must have that:
Thus, the correct answer is the statement:
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