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=31x3+25x2−24x+10Use calculus to find the values of xxx for which the system's potential energy is stationary.
By using the second derivative, determine the nature of each of these stationary points.
Practise Edexcel A Level Maths Differentiation with exam-style questions for A Level Maths. 311 questions 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, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
