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.
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.