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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

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Answer

To find the derivative of the function, we apply the power rule. The function is given as:

$f(x) = 3x + x^3$

Differentiating term by term gives:

$f'(x) = 3 + 3x^{2}$

So, the derivative of the function is:

$f'(x) = 3 + 3x^{2}$

Step 2

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Answer

Given that f'(x) = 15, we can set up the equation:

$3 + 3x^{2} = 15$

To solve for x, we rearrange this equation:

Subtract 3 from both sides: $3x^{2} = 15 - 3$ $3x^{2} = 12$
Divide both sides by 3: $x^{2} = 4$
Taking the square root of both sides gives us: $x = ext{±2}$ Since x > 0, we take: $x = 2$

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