Using differentiation, show that f(x) = 2x^3 - 12x^2 + 25x - 11 is an increasing function.

First compute the derivative of f(x) using the power rule on each term. f(x) = 2x^3 - 12x^2 + 25x - 11 so f'(x) = 6x^2 - 24x + 25. Now complete the square for the derivative. f'(x) = 6 * ((x-2)^2 - 4) + 25 = 6 * (x-2)^2 - 24 + 25 = 6 * (x-2)^2 + 1. Now observe that the first term is >= 0 since it is the result of a square multiplied by the positive constant 6. The second term, 1, is positive. Hence the whole expression is positive for any x. So we've shown that f'(x) > 0 for any x, so the function f(x) is increasing.

MT
Answered by Michael T. Further Mathematics tutor

3147 Views

See similar Further Mathematics GCSE tutors

Related Further Mathematics GCSE answers

All answers ▸

Differentiate y = x*cos(2x)


Use differentiation to show the function f(x)=2x^3–12x^2+25x–11 is an increasing function for all values of x


Express (7+ √5)/(3+√5) in the form a + b √5, where a and b are integers.


The equation of the line L1 is y = 3x – 2 The equation of the line L2 is 3y – 9x + 5 = 0 Show that these two lines are parallel.


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