The curve with equation $y = f(x)$ passes through the point $(-1, 0)$ - Edexcel - A-Level Maths Pure - Question 9 - 2011 - Paper 2
Question 9
The curve with equation $y = f(x)$ passes through the point $(-1, 0)$.
Given that
$f'(x) = 12x^2 - 8x + 1$
find $f(x)$.
Worked Solution & Example Answer:The curve with equation $y = f(x)$ passes through the point $(-1, 0)$ - Edexcel - A-Level Maths Pure - Question 9 - 2011 - Paper 2
Step 1
Integrate $f'(x)$
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Answer
To find f(x), we need to integrate f′(x).
f(x)=∫(12x2−8x+1)dx=4x3−4x2+x+c
where c is the constant of integration.
Step 2
Use the point $(-1, 0)$
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Answer
Now, we substitute the point (−1,0) into f(x):
f(−1)=0=4(−1)3−4(−1)2+(−1)+c
This simplifies to:
0=−4−4−1+c
0=−9+c
So, we find:
c=9
Step 3
Final function $f(x)$
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Answer
Now substituting c back into the function, we get:
