How would you show the equation f(x) = 2x – 10 sin x – 2 has a root between 2 and 3 (where x is measured in radians)

With these kind of problems you are looking to find 2 values with which the output of the function is positive for one and negative for the other. In this scenario they have given 2 values 2 and 3 so the first step would be to input those to the equation.f(2) = -7.092974268... f(3) = 4.588799919...Since there is a sign change between the 2 values and f is a continuous function,there is therefore a root between the values between 2 and 3. It is vital when answering an exam question on this to give this reason as to why there is a root there otherwise you will normally not receive full marks.

KN
Answered by Kelvin N. Further Mathematics tutor

3266 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

prove by induction that, f(n) = 2^(3n+1) + 3(5^(2n+1)) is divisible by 17 for all n>0.


Find the eigenvalues and eigenvectors of the matrix M , where M{2,2} = (1/2 2/3 ; 1/2 1/3) Hence express M in the form PDP^-1 where D is a diagonal matrix.


The curve C has polar equation 'r = 3a(1 + cos(x)). The tangent to C at point A is parallel to the initial line. Find the co-ordinates of A. 0<x<pi


Given sinhx = 0.5(e^x - e^-x), express its inverse, arcsinhx in terms of x.


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:

© 2026 by IXL Learning