For a curve of gradient dy/dx = (2/(x^2))-x/4, determine a) d^2y/dx^2 b) the stationary point where y=5/2 c) whether this is a maximum or minmum point and d) the equation of the curve

a) Differentiating gives d2y/dx2=-4x-3-1/4

b) Let dy/dx=0 and rearrange to find x=2

c) Inserting x=2 into d2y/dx2=-4x-3-1/4 will show that d2y/dx2 is smaller than zero so this is a maximum stationary point.

d) To find the original equation of the curve, dy/dx must be intetgrated which gives y=-2x-1-x2/8+c

Substituting in x=2 when y=5/2 gives 2.5=-1-0.5+c

Rearrange to give c=4

So the final equation is y=-2x-1-x2/8+4

Answered by Katie M. Maths tutor

5288 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

When I integrate by parts how do I know which part of the equation is u and v'?


A curve is defined for x > 0. The gradient of the curve at the point (x,y) is given by dy/dx = x^(3/2)-2x. Show that this curve has a minimum point and find it.


Find the gradient of the function f(x,y)=x^3 + y^3 -3xy at the point (2,1), given that f(2,1) = 6.


If f(x) = x^2 - 3x + 2, find f'(x) and f''(x)


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