A curve has parametric equations: x = 3t +8, y = t^3 - 5t^2 + 7t. Find the co-ordinates of the stationary points.

First differentiate: dx/dt = 3,   dy/dt = 3t2 - 10t + 7

Using the chain rule: dy/dx = dy/dt * dt/dx = (3t2 - 10t + 7)/3 

At stationary points, the gradient is equal to zero: 3t2 - 10t + 7 = 0

Solve for t using the quadratic formula and substituting these values: a = 3, b = -10, c = 7

Solutions: t = 7/3 and 1

For the co-ordinates, substitute the values of t into the parametric equations: (15, 49/27) and (11, 3)

RB
Answered by Robbie B. Maths tutor

5379 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Why do we need the constant of integration?


What is the equation of the tangent at the point (2,1) of the curve with equation x^2 + 3x + 4.


Find the minimum and maximum points of the graph y = x^3 - 4x^2 + 4x +3 in the range 0<=x <= 5.


How do you differentiate using the chain rule?


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning