4. (a) Differentiate to find $f'(x)$ - Edexcel - A-Level Maths Pure - Question 6 - 2008 - Paper 1
Question 6
4.
(a) Differentiate to find $f'(x)$.
Given that $f'(x) = 15$,
(b) find the value of $x$.
Worked Solution & Example Answer:4. (a) Differentiate to find $f'(x)$ - Edexcel - A-Level Maths Pure - Question 6 - 2008 - Paper 1
Step 1
Differentiate to find $f'(x)$
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Answer
To differentiate the function ( f(x) = 3x + x^3 ), we apply the power rule. The derivative of ( 3x ) is ( 3 ), and the derivative of ( x^3 ) is ( 3x^2 ). Therefore,
[
f'(x) = 3 + 3x^2.
]
Step 2
find the value of $x$
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Answer
Now we need to find the value of ( x ) given that ( f'(x) = 15 ):
Set the derivative equal to 15:
[ 3 + 3x^2 = 15 ]
Subtract 3 from both sides:
[ 3x^2 = 12 ]
Divide by 3:
[ x^2 = 4 ]
Take the square root of both sides:
[ x = 2 ]
Since ( x > 0 ), we take the positive root. Thus, the value of ( x ) is ( 2 ).
