Given:
$f(x)=x(x-3)^2$ with
$f'(1)=f'(3)=0$ and $f(1)=4$
8.1 Show that $f$ has a point of inflection at $x = 2$ - NSC Mathematics - Question 8 - 2017 - Paper 1
Question 8
Given:
$f(x)=x(x-3)^2$ with
$f'(1)=f'(3)=0$ and $f(1)=4$
8.1 Show that $f$ has a point of inflection at $x = 2$.
8.2 Sketch the graph of $f$, clearly indic... show full transcript
Worked Solution & Example Answer:Given:
$f(x)=x(x-3)^2$ with
$f'(1)=f'(3)=0$ and $f(1)=4$
8.1 Show that $f$ has a point of inflection at $x = 2$ - NSC Mathematics - Question 8 - 2017 - Paper 1
Step 1
Do you agree with Claire? Justify your answer.
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Answer
I do not agree with Claire; her statement is incorrect. To evaluate f′(2), we need to calculate it as follows:
f′(2)=3(2)2−12(2)+9=12−24+9=−3
This indicates that f′(2)=−3, not 1. Thus, Claire's assertion that f′(2)=1 is false.
