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
3703 Views
See similar Further Mathematics A Level tutorsRelated Further Mathematics A Level answers
All answers ▸It is given that f(x)=(x^2 +9x)/((x-1)(x^2 +9)). (i) Express f(x) in partial fractions. (ii) Hence find the integral of f(x) with respect to x.
Find the general solution to: d^(2)x/dt^(2) + 7 dx/dt + 12x = 2e^(-t)
Write 1 + √3i in modulus-argument form
(FP1) Given k = q + 3i and z = w^2 - 8w* - 18q^2 i, and if w is purely imaginary, show that there is only one possible non-zero value of z