I have this question in my applied mathematics course.
Suppose that $ x'(t_1)\neq0$ . Show that we can solve the equation $ x=x(t)$ for $ t=t(x)$ in a neighbourhood of the point $ x_1=x(t_1)$ . We were given a hint: If $ x'(t_1)\neq0$ , then $ x(t)$ is strictly monotonic function of $ t$ in neighbourhood of $ t=t_1$ .
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