A research probe measures the signal intensity I I\,I at a distance x x\,x from a source. The intensity is modeled by the function
I=54x4−485x+500+32x2x≠0 I = 54x^4 - 485x + 500 + \frac{32}{x^2} \quad x \neq 0 I=54x4−485x+500+x232x=0Find dIdx\displaystyle \frac{dI}{dx}dxdI.
Hence find the coordinates of the stationary points of the curve.
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.