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 AQA A Level Maths 1.10 G: Differentiation with exam-style questions for A Level Maths. 321 questions 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), matched to the AQA A Level Maths (7357) 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.
