f(x) = 2x^3+6x^2-18x+1. For which values of x is f(x) an increasing function?

For f(x) to be an increasing function at x, the derivative of f(x) must be greater than 0. So, the answer to this question will be revealed by solving the equation f'(x) > 0 for x.By differentiating the terms of the polynomial f(x), we get f'(x) = 6x2+12x-18 > 0. To find the range(s) of x for which this is true, we can solve the quadratic 6x2+12x-18 = 0 to find the points at which it either starts or stops becoming true, and then use what we know about the graph to find the ranges.By first removing common factors from both sides:6(x2+2x-3) = 6(0)x2+2x-3 = 0and then factorising the quadratic:(x+3)(x-1) = 0we can get the solutions:x = -3, x = 1.So, by looking at the graph we can see that the regions we need are before the first intersection point (x = -3) and after the second (x = 1), so we get the solutions:x < -3, x > 1.

NW
Answered by Nikhil W. Further Mathematics tutor

3966 Views

See similar Further Mathematics GCSE tutors

Related Further Mathematics GCSE answers

All answers ▸

Solve these simultaneous equations: 3xy = 1, and y = 12x + 3


Find the x and y coordinates of the minimum of the following equation: y = x^2 - 14x + 55.


Find the coordinates of any stationary points of the curve y(x)=x^3-3x^2+3x+2


In the expansion of (x-7)(3x**2+kx-3) the coefficient of x**2 is 0. i) Find the value of k ii) Find the coefficient of x. iii) write the fully expanded equation in terms of x


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 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences