A magnetic flux contour line CCC within a specialized superconducting alloy is modeled by the equation
y2+60x−x2y=k,y>0 y^2 + 60x - x^2 y = k, \quad y > 0 y2+60x−x2y=k,y>0where kkk is a constant and xxx and yyy represent spatial coordinates measured in micrometers.
Find dydx\dfrac{dy}{dx}dxdy in terms of xxx and yyy.
The point P(p,10)P(p, 10)P(p,10), where ppp is a constant, lies on CCC. Given that PPP is the minimum turning point on CCC,
find
(i) the value of ppp
(ii) the value of kkk
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.
