Answer true or false. The Intermediate-Value Theorem can be used to show that the equation x⁵ = cos x has at least one solution on the interval [-5 $\pi$/6, 5 $\pi$/6].

Question

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The Intermediate-Value Theorem states that if a continuous function takes on values of opposite sign at two points in an interval, then it must take on the value zero at some point within that interval. In this case, x⁵ = cos x is a continuous function and it is easy to see that it takes on values of opposite signs at -5π/6 and 5π/6. Therefore, by the Intermediate-Value Theorem, it must have at least one solution on the interval [-5π/6, 5π/6].

Answer True or False π\piπ /6, 5 π\piπ /6]

Answer True or False $\pi$ /6, 5 $\pi$ /6]