Given the function y=(x+1)(x-2)^2 find i) dy/dx ii) Stationary points and determine their nature

Here we have a function made from the product of two functions, so we canuse the product differenciation rule.

y=uv  =>  dy/dx=udv/dx + vdu/dx

Therefore dy/dy=(x-2)^2 + 2(x-2)(x+1)

Stationary points occur when the gradient is zero, we solve for (x-2)^2 + 2(x-2)(x+1)=0 which gives (0,4), (2,0)

Solving for nature of stationary point we find the second derivative d^2y/dx^2=6x-6

When x=0 we get a maximum, when x=2 we get a minimum point.

Answered by Russell B. Maths tutor

4410 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Given that z=sin(x)/cos(x), show that dz/dx = sec^2(x).


By writing tan x as sin x cos x , use the quotient rule to show that d dx ðtan xÞ ¼ sec2 x .


Express 4x/(x^2-9)-2/(x+3) as a single fraction in its simplest form


How do I find the maximum/minimum of a function?


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