THINGS WRITTEN ON THE IMAGE ARE INCORRECT

The graph of f(x) = 4x+e^(5sin(x)) is rotated counterclockwise about the origin through an acute angle ?. What is the largest value of ? for which the rotated graph is still the graph of a function? What about if the graph is rotated clockwise?

What is the largest value of ? 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 y=f(x), which is (answer) and the minimal slope which is (answer 2).

Thus the maximal acute angle through which the graph can be rotated counterclockwise is ? = (Answer 3) degrees

Thus the maximal acute angle through which the graph can be rotated clockwise is ? = (answer 4) degrees. (Your answer should be negative to indicate the clockwise direction.)

(1 point) The graph of f(x) = 4x + 5 sin(1) is rotated counterclockwise about the origin through an acute angle 0. What is the largest value of O 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 y = f(c), which is |4 + e^5sin(x) *5cos(x) , and the minimal slope which is 0 Thus the maximal acute angle through which the graph can be rotated counterclockwise is d = 0 degrees. Thus the maximal acute angle through which the graph can be rotated clockwise is 0 = 0 degrees. (Your answer should be negative to indicate the clockwise direction.) Note that a line y = mc + 6 makes angle o with the horizontal, where tan(a) = m. 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 y = mc + 6 of a fixed slope m intersect a graph of y = f() in at most one point, what can you say about rotating the graph of y = f(I)? 2. If some line y = me + bintersects the graph of y = f(@) in two or more points, what can you say about rotating the graph of y = f(I)? 3. If some line y = max + b intersects the graph of y = f(@) in two or more points, what does the Mean Value Theorem tell us about f' (I)