Determine the coordinates of all the stationary points of the function f(x) = (1/3)*x^3+x^2-3*x+1 and state whether they are a maximum or a minimum.

To find the answer you must first differentiate the function and set this equal to zero. This forms the quadratic equation x^2+2x-3=0 which can then be solved either by factorisation or by using the quadratic formula. This enables you to find the x-coordinates of the two stationary points which can then be substituted back into the original equation to find the y-coordinates of the stationary points. The coordinates of the stationary points are (1, -2/3) and (-3, -8).To find the nature of the stationary points you must find the second differential of the original function which is f”(x)=2x+2. Then you substitute the x-coordinates into this function and if f”(x)<0 the point is a maximum, if f”(x)>0 then the point is a minimum. Therefore, we can determine that (-3, -8) is a maximum and (1, -2/3) is a minimum.

AN
Answered by Alex N. Maths tutor

3659 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

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.


The curve C has equation y = 3x^4 – 8x^3 – 3 (a) Find (i) dy/dx (ii) d^2y/dx^2 (3 marks) (b) Verify that C has a stationary point when x = 2 (2marks) (c) Determine the nature of this stationary point, giving a reason for your answer. (2)


Show that the curve with equation y=x^2-6x+9 and the line with equation y=-x do not intersect.


Circle C has equation x^2 + y^2 - 6x + 4y = 12, what is the radius and centre of the circle


We're here to help

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

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning