Mathematics

Problem

Let

f(x)=x^{3}-4x

and

g(x)=\sin x

, where

x

is measured in radians. a. Evaluate

f(0)-g(0)

and

f(1)-g(1)

. Determine the sign of each difference. b. Use your work in part (a) to identify an interval of length

1

that contains at least one solution to the equation

f(x)=g(x)

. c. Compute

f(0.5)-g(0.5)

. Use this additional value to narrow the location of a solution to an interval of length at most

0.5

, and clearly state that interval.