A curve is given by the equation y = (1/3)x^3 -4x^2 +12x -19. Find the co-ordinates of any stationary points and determine whether they are maximum or minimun points.

Stationary points - dy/dx =0dy/dx = x2 -8x +12 ( differentiating- early a level skill). Solving x2 -8x +12=0 gives x=6, x=2 (solving quadratics- gcse skill). Subbing these values back into the original equation gives the co-ordinates of the stationary points- (2,-8), (6,-19)To determine whether they are maximum or minimum points we need to find the second derivative (differentiation)d2y/dx2 = 2x-8.Subbing in our x co-ordinate for the stationary point (2,-8) gives d2y/dx2= -4. Since this is negative, (2,-8) is a maximum point. Similarly, subbing in the x value of our other stationary point gives d2y/dx2= 4. Since this is positive, (6,-19) is a minimum point.

JC
Answered by Joseph C. Maths tutor

2914 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Find the range of values of k for which x²+kx-3k<5 for some x, i.e. the curve y=x²+kx-3k goes below y=5


A factory produces cartons each box has height h and base dimensions 2x, x and surface area A. Given that the capacity of a carton has to be 1030cm^3, (a) Using calculus find the value of x for which A is a minimum. (b) Calculate the minimum value of A.


Differentiate a^x


Find the roots of y=x^{2}+2x+2


We're here to help

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

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences