A specialized surveillance drone follows a path CCC in a 2D plane defined by the parametric equations
x=3t2+1,y=2t3−15t+k x = 3t^2 + 1, \quad y = 2t^3 - 15t + k x=3t2+1,y=2t3−15t+kwhere kkk is a constant and t≥0t \ge 0t≥0 represents time.
Find an expression for dydx\frac{dy}{dx}dxdy in terms of ttt.
The line lll is the normal to the path at point AAA where t=1t = 1t=1.
Given that lll is also a tangent to the path at point BBB where t=Tt = Tt=T,
show that TTT is a solution of the equation
6T2−4T−15=0 6T^2 - 4T - 15 = 0 6T2−4T−15=0Hence find the xxx-coordinate of point BBB, justifying your answer.
Given that the yyy-intercept of the line lll is 13\frac{1}{3}31,
find the value of kkk.
Practise Edexcel A Level Maths Differentiation with exam-style questions for A Level Maths. 327 questions covering 12.1 Gradients of Curves, 12.2 Differentiation from first principles, 12.3 Differentiating x^n, 12.4 Differentiating Quadratics, 12.5 Differentiating functions with two or more terms, 12.6 Gradients, Tangents and Normals, 12.7 Increasing and Decreasing Functions, 12.8 Second Order Derivatives, 12.9 Stationary Points, 12.10 Sketching Gradient Functions, and 12.11 Modelling with Differentiation, matched to the Edexcel A Level Maths (9MA0) 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.
