Find the coordinates of the stationary point on the curve with equation $y = 2x^2 - 12x$.
- Edexcel - A-Level Maths Pure - Question 3 - 2005 - Paper 2
Question 3
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 3 - 2005 - Paper 2
Step 1
Step 1: Find the derivative of the function
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Answer
To locate the stationary points, we first need to find the derivative of the function. Differentiating the equation:
dxdy=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 x where the slope is zero:
4x−12=0.
Solving this equation gives:
4x=12⇒x=3.
Step 3
Step 3: Find the $y$ coordinate
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Answer
Now that we have x=3, we can substitute this back into the original equation to find the y coordinate:
y=2(32)−12(3)=2(9)−36=18−36=−18.
Step 4
Step 4: State the coordinates of the stationary point
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Answer
Thus, the coordinates of the stationary point on the curve are (3,−18).
