Find the coordinates of the turning point on the curve with equation
$y = 9 + 18x - 3x^2$ - Edexcel - GCSE Maths - Question 4 - 2021 - Paper 1
Question 4
Find the coordinates of the turning point on the curve with equation
$y = 9 + 18x - 3x^2$.
You must show all your working.
Worked Solution & Example Answer:Find the coordinates of the turning point on the curve with equation
$y = 9 + 18x - 3x^2$ - Edexcel - GCSE Maths - Question 4 - 2021 - Paper 1
Step 1
Differentiate the expression
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Answer
To find the turning point, we first differentiate the equation.
The derivative of the function is given by:
y' = rac{dy}{dx} = 18 - 6x
Setting the derivative equal to zero to find the turning points:
18−6x=0
Step 2
Solve for x
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Answer
From the equation 18−6x=0, we can solve for x:
6x=18x=3
Step 3
Substitute x back into the original equation to find y
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Answer
Next, we substitute x=3 back into the original equation to find the corresponding y value:
y=9+18(3)−3(32)y=9+54−27y=36
Step 4
Final coordinates
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Answer
Thus, the coordinates of the turning point are (3,36).
