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.
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.
