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Find the coordinates of the stationary point on the curve with equation $y = 2x^2 - 12x$. - Edexcel - A-Level Maths Pure - Question 2 - 2005 - Paper 2

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Find the coordinates of the stationary point on the curve with equation $y = 2x^2 - 12x$.

Worked Solution & Example Answer:Find the coordinates of the stationary point on the curve with equation $y = 2x^2 - 12x$. - Edexcel - A-Level Maths Pure - Question 2 - 2005 - Paper 2

Step 1

Step 1: Differentiate the equation

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Answer

To find the stationary points, we need to calculate the derivative of the function. The equation given is:

y=2x2−12xy = 2x^2 - 12x

Differentiating with respect to xx, we get:

dydx=4x−12\frac{dy}{dx} = 4x - 12

Step 2

Step 2: Set the derivative to zero

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Answer

Next, we set the derivative equal to zero to find the values of xx at the stationary points:

4x−12=04x - 12 = 0

Step 3

Step 3: Solve for $x$

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Answer

Solving the equation:

4x=124x = 12

Thus,

x=3x = 3

Step 4

Step 4: Find the corresponding $y$ value

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Answer

Now, we substitute x=3x = 3 back into the original equation to find the corresponding yy value:

y=2(3)2−12(3)=18−36=−18y = 2(3)^2 - 12(3) = 18 - 36 = -18

Step 5

Final Answer

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Answer

The coordinates of the stationary point are:

(3,−18)(3, -18)

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