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

Related Further Mathematics A Level answers

All answers ▸

How to solve a standard first order differential equation?


Find the GS to the following 2nd ODE: d^2y/dx^2 + 3(dy/dx) + 2 = 0


A particle is moving in a straight line with simple harmonic motion. The period of the motion is (3pi/5)seconds and the amplitude is 0.4metres. Calculate the maximum speed of the particle.


How do I sketch the locus of |z - 5-3i | = 3 on an Argand Diagram?