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.
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Answered by Kelvin N. • Further Mathematics tutor
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