Transcribed Image Text: Consider the following equation.
cos x = x3
(a) Prove that the equation has at least one real root.
? 0?v -0.46, there is a number
f(x) = cos x –- x³ is continuous on theinterval [0, 1], f(0) =
c in (0, 1) such that f(c) = 0 by the Intermediate Value Theorem. Thus, there is a root of the equation cos x – x =
? v0, and f(1) = cos 1 – 1 = -0.46 ? v 0. Since
or cos x = x, in the interval (0, 1).
(b) Use your calculator to find an interval of length 0.01 that contains a root. (Enter your answer using interval notation.)