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A curve has equation $y = x^5 + 4x^3 + 7x + q$ where $q$ is a positive constant - AQA - A-Level Maths Pure - Question 2 - 2018 - Paper 3
Question 2
A curve has equation $y = x^5 + 4x^3 + 7x + q$ where $q$ is a positive constant. Find the gradient of the curve at the point where $x = 0$. Circle your answer.
Worked Solution & Example Answer:A curve has equation $y = x^5 + 4x^3 + 7x + q$ where $q$ is a positive constant - AQA - A-Level Maths Pure - Question 2 - 2018 - Paper 3
Step 1
Find the gradient of the curve at the point where $x = 0$
Answer
To find the gradient of the curve, we need to differentiate the equation with respect to :
rac{dy}{dx} = 5x^4 + 12x^2 + 7
Next, we evaluate the derivative at the point where :
rac{dy}{dx} \bigg|_{x=0} = 5(0)^4 + 12(0)^2 + 7 = 7
Therefore, the gradient of the curve at the point where is 7.