using the intermediate value theorem

Question

Using the Intermediate Value Theorem, consider the statement "The cosine of t is equal to t cubed."

1. Write a mathematical equation of the statement.
2. Prove that the equation in part (a) has at least one real solution.
3. Use a calculator to find an interval of length 0.01 that contains a solution

Answer 1

f(t)=cos(t)-t³

f(0)=1 and f(π/2)=-(π/2)³

Since f is continuous on the whole real line, there is a root between 0 and π/2.

I will leave the last part of the question for you to compute.