How do I find the turning points of a curve?

At turning points, the gradient is 0. Differentiating an equation gives the gradient at a certain point with a given value of x. To find turning points, find values of x where the derivative is 0.Example:y=x2-5x+6dy/dx=2x-52x-5=0x=5/2Thus, there is on turning point when x=5/2. To find y, substitute the x value into the original formula. y=(5/2)2-5x(5/2)+6y=99/4Thus, turning point at (5/2,99/4).Additional pointsOnce turning point is identified, you can work out if it is a maximum or minimum by finding d2y/dx2. d2y/dx2<0 - maximumd2y/dx2.>0 - minimumThus for our example aboved2y/dx2=2 - minimum

Answered by Shannon G. Maths tutor

82730 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

If n is an integer such that n>1 and f(x)=(sin(n*x))^n, what is f'(x)?


The straight line with equation y=3x-7 does not cross or touch the curve with equation y=2px^2-6px+4p, where p is a constant.(a) Show that 4p^2-20p+9<0 (b) Hence find the set of possible values for p.


How do I identify that the coordinate (2,3) is the maximum point of the curve f(x)?


Find the stationary pointsof the following: (y = x^3 - x^2 -16 x -17) and determine if each point is a maximum or minimum.


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 2013–2024

Terms & Conditions|Privacy Policy