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Differentiation

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Question 394

An ungraduated coordinate diagram shows arrowed x- and y-axes, the origin O, and a curve for t > 0 that dips below the x-axis before rising into the first quadrant.

The diagram shows the curve given parametrically by the equations x=4t2x = 4t^2x=4t2, y=t(t2−12)y = t(t^2 - 12)y=t(t2−12), for t>0t > 0t>0

a.

Show that dydx=3t2−128t\displaystyle \frac{dy}{dx} = \frac{3t^2 - 12}{8t}dxdy​=8t3t2−12​

[3]
b.

Find the equation of the line through (0,1)(0, 1)(0,1) which is parallel to the tangent to the curve at the point (36,−9)(36, -9)(36,−9)

[3]
c.

Find the cartesian equation of the curve.

[3]
Markscheme

Differentiation Questions

  1. A Level
  2. /Maths
  3. /Differentiation

717 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.

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