At x=3, is the polynomial y= (4/3)x^3 -6x^2 + 11 at a maxima or minima?

First, take the first differential: y' = 4x^2 -12x. At x=3 y'= 0 so therefore the function is at a point of inflection. Taking the second derivative: y'' = 8x -12. At x=3 y''= 12. As 12 is greater than 0, the polynomial is at a minimum. If the second differential was less than 0, it would be a point of maximum and if it equaled 0 then the test fails. We must find out by comparing the sign of values of the first derivative slightly less and slightly more than the value.

JT
Answered by James T. Maths tutor

3580 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

A circle, C, has an equation: x^2 + y^2 - 4x + 10y = 7 . Find the centre of the circle and its radius?


A curve has equation y = 20x −x^2 −2x^3 . Find its stationary point(s).


The equation (t – 1)x^2 + 4x + (t – 5) = 0, where t is a constant has no real roots. Show that t satisfies t2–6t+1>0


Find d/dx (ln(2x^3+x+8))


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