# Rotating a Graph?

Calculus Level 5

The above shows twos functions on a same Cartesian Plane: $$f(x)$$ and $$f^\theta (x)$$ colored blue and red respectively.

Let $$f(x)=x^3-6x^2+6x+1$$

Define $$f^{\theta}(x)$$, where $$\theta \geq 0$$, as the new graph obtained by rotating the graph of $$f(x)$$ $$\theta$$ degrees about the origin ($$0,0$$) in the clockwise direction.

Find the maximum value of $$\theta_M$$ such that for all values of $$0<\theta<\theta_M$$, $$f^{\theta}(x)$$ has every value of $$x$$ paired with only one $$y$$ (more simply, no two points can have the same $$x$$-coordinate).

Input your answer as $$\lfloor 100\cdot\theta_m \rfloor$$. Where $$\lfloor x \rfloor$$ is the floor function which means the greatest integer less than or equal to $$x$$.

This is part of the set Trevor's Ten

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