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Given $y = x^3 + 4x + 1$, find the value of $ \frac{dy}{dx} $ when $x = 3$. - Edexcel - A-Level Maths Pure - Question 3 - 2013 - Paper 2

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$Given-$y-=-x^3-+-4x-+-1$,-find-the-value-of-$-\frac{dy}{dx}-$-when-$x-=-3$.-Edexcel-A-Level Maths Pure-Question 3-2013-Paper 2.png$

Given $y = x^3 + 4x + 1$, find the value of $ \frac{dy}{dx} $ when $x = 3$.

Worked Solution & Example Answer:Given $y = x^3 + 4x + 1$, find the value of $ \frac{dy}{dx} $ when $x = 3$. - Edexcel - A-Level Maths Pure - Question 3 - 2013 - Paper 2

Step 1

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Answer

To find ( \frac{dy}{dx} ), we will differentiate the function:

[ \frac{dy}{dx} = \frac{d}{dx}(x^3 + 4x + 1) = 3x^2 + 4. ]

Step 2

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Answer

Now, we will substitute ( x = 3 ) into the derivative to find the value:

[ \frac{dy}{dx} = 3(3)^2 + 4 = 3(9) + 4 = 27 + 4 = 31. ]

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