Differentiation
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Question 389
The diagram shows the curve given parametrically by the equations x=4t2x = 4t^2x=4t2, y=t(t2−8)y = t(t^2 - 8)y=t(t2−8), for t>0t > 0t>0
a.[3]
Show that dydx=3t2−88t\displaystyle \frac{dy}{dx} = \frac{3t^2 - 8}{8t}dxdy=8t3t2−8
b.[3]
Find the coordinates of the point on the curve at which the tangent to the curve is parallel to the line 3x−12y+8=03x - 12y + 8 = 03x−12y+8=0
c.[3]
Find the cartesian equation of the curve.
Differentiation Questions
649 exam-style questions on Edexcel A Level Maths Differentiation, covering 9.1 Differentiating sin x and cos x, 9.2 Differentiating exponentials and logarithms, 9.3 The Chain Rule, 9.4 The Product Rule, 9.5 The Quotient Rule, 9.6 Differentiating Trigonometric Functions, 9.7 Parametric Differentiation, 9.8 Implicit Differentiation, 9.9 Using Second Derivatives, and 9.10 Rates of Change. Each one has a worked solution and a mark scheme showing where the marks go.