The graph of
f(x) = -7 x + e^{3 x - 50 x^2}
is rotated counterclockwise about the origin through an acute angle \theta .
What is the largest value of \theta for which the rotated graph is still
the graph of a function? What about if the graph is rotated clockwise?

To answer this question we need to find the maximal slope of

Thus the maximal acute angle through which the graph can be rotated counterclockwise
is

Thus the maximal acute angle through which the graph can be rotated clockwise
is

Note that a line

** Hints: ** Recall that a graph of a function is characterized by the property that every vertical line intersects the graph in at most one point. In view of this:

1. If ALL lines

2. If some line

3. If some line

You can earn partial credit on this problem.