THINGS WRITTEN ON THE IMAGE ARE INCORRECT The graph of f ( x ) = 4 x + e^( 5sin(
ID: 2881391 • Letter: T
Question
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 5 sin( f(z) is rotated counterclockwise about the origin through an acute angle 6. What is the largest value of 6for 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(r) which is 4+en5sincx)* 5cos(x) and the minimal slope which is 0 Thus the maximal acute angle through which the graph can be rotated counterclockwise is 0 0 degrees degrees. our Thus the maximal acute angle through which the graph can be rotated clockwise is 0 answer should be negative to indicate the clockwise direction.) Note that a line y mar +bmakes angle a th 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 AL lines y mr bof a fixed slope mintersect a graph of y f(z) n at most one point, what can you say about rotating L the graph of y f(z)? 2. If some line y mar bintersects the graph of y f(z) in two or more points, what can you say about rotating the graph of y f(z)? mar bintersects the graph of y f(z) in two or more points some line y hat does the Mean Value Theorem tell us about f (z)?Explanation / Answer
F(x) = 4x+e (5sin(x))
F’(x) = 4 + e (5sin(x)) 5 cos(x)
To find the extremum point of F(x), Let F’(x) =0
Therefore, 4 + e (5sin(x)) 5 cos(x) = 0
At x= /2 F’(x) = 4 (maximum slope) and at x= F’(x) = 3 (minimum slope)
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