A curve C has equation y = x^2 − 2x − 24 x^(1/2), x > 0 (a) Find (i) dy/d x (ii) d^2y/dx^2 (b) Verify that C has a stationary point when x = 4 (c) Determine the nature of this stationary point, giving a reason for your answer.

(a) i) dy/dx= 2x-2-12x-1/2ii) d2 y/dx2 = 2+6x-3/2(b) Substitute x=4 into dy/dx= 2x-2-12x-1/2 Show that dy/dx= 0 and state 'hence there is a stationary point' (c) Substitute x=4 into d2 y/dx2 = 2+6x-3/2 (=2.75) d2 y/dx2>0 and state 'hence minimum'

Answered by Maths tutor

8573 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Find the x co-ordinates of the stationary points of the graph with equation y = cos(x)7e^(x). Give your answer in the form x = a +/- bn where a/b are numbers to be found, and n is the set of integers.


find the value of dy/dx at the point (1,1) of the equation e^(2x)ln(y)=x+y-2


integrate cos^2(2x)sin^3(2x) dx


Form the differential equation representing the family of curves x = my , where, m is arbitrary constant.


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