f(x) = 3x + x^3,
x > 0 - Edexcel - A-Level Maths Pure - Question 6 - 2008 - Paper 1
Question 6
f(x) = 3x + x^3,
x > 0.
(a) Differentiate to find f'(x).
Given that f'(x) = 15,
(b) find the value of x.
Worked Solution & Example Answer:f(x) = 3x + x^3,
x > 0 - 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, we apply the power rule to each term of the function.
Starting with: f(x)=3x+x3
The derivative, denoted as f'(x), is obtained as follows:
The derivative of 3x is 3.
The derivative of x^3 is (3x^{2}).
Thus, combining these results, we have: f′(x)=3+3x2
Step 2
find the value of x.
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Answer
Given that f'(x) = 15, we substitute this into our expression for f'(x): 3+3x2=15
Subtract 3 from both sides: 3x2=12
Dividing both sides by 3 gives: x2=4
Taking the square root of both sides results in: x=2
Since we are given x > 0, we ignore the negative root.
