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1.10 G: Differentiation

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Question 201

The potential energy, VVV Joules, of a mechanical system depends on a configuration parameter xxx according to the model:

V=13x3+52x2−24x+10 V = \frac{1}{3}x^3 + \frac{5}{2}x^2 - 24x + 10 V=31​x3+25​x2−24x+10
a.

Use calculus to find the values of xxx for which the system's potential energy is stationary.

[3]
b.

By using the second derivative, determine the nature of each of these stationary points.

[3]
Markscheme

1.10 G: Differentiation Questions

  1. A Level
  2. /Maths
  3. /1.10 G: Differentiation

375 exam-style questions on AQA A Level Maths 1.10 G: Differentiation, covering 1.10.1 The derivative and second derivative, 1.10.2 Differentiating standard functions, 1.10.3 Applications of differentiation, 1.10.4 Product, quotient and chain rules (A-level only), 1.10.5 Implicit and parametric differentiation (A-level only), and 1.10.6 Constructing differential equations (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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