A curve is defined by the parametric equations x = 2t and y = 4t^2 + t. Find the gradient of the curve when t = 4

the gradient of the curve = dy/dx
and dy/dx = (dy/dt)(dt/dx)
dy/dt = 8t + 1
dx/dt = 2 therefore dt/dx = 1/2
dy/dx as above = (8t + 1) * 1/2 = (8t + 1)/2
where t = 4, dy/dx = (8*4 + 1)/2 = (32 + 1)/2 = 33/2

Answered by Angus B. Maths tutor

4976 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

What is Differentiation?


f(x) is defined by f(x) = 3*x^3 + 2*x^2 - 7*x + 2. Find f(1).


The equation f(x) =x^3 + 3x is drawn on a graph between x = 0 and x = 2. The graph is then rotated around the x axis by 2π to form a solid. What is the volume of this solid?


a curve has an equation: y = x^2 - 2x - 24x^0.5 x>0 find dy/dx and d^2y/dx^2


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences