Calculate the angle of inclination?
How do you calculate numbers 2c) and 2d) in this problem? I can't figure it out. Where is the given angle?
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As a reminder: The derivative of a function at a certain point x is the slope of the tangent to the function at the point in question P(x | f(x)) and it holds
In part c) the intersection point of the function with the y-axis is at x=0 (ie the origin) and therefore
(arctan is often known today as tan -1 because the inverse function of the tangent is often labeled this way on pocket calculators)
This should also make it clear what has to be solved in part d) : Find the x at which
applies (there are 2 solutions if the angle of inclination of the tangents is understood as the acute angle to the x-axis)
Sketch for c)
Sketch for d)
In d) I am not sure whether one should not name only one
Or as a question: Does the parabola not have a slope angle of 260°
Well, I understand that people mean the acute angle, which is why I use the phrase " if you… understand the acute angle to the x-axis," knowing that there are different interpretations. My understanding has always been that the angle on the right is -60°. Then the next person comes along and says: "We're only looking for angles between 0° and 180°," and I say, "Okay—the vertex angle is then +60°, or whatever, or something else." And since teachers sometimes have very specific ideas and preferences anyway, the person asking the question should choose what applies to their class.
Where is the angle?
Slope is defined as the slope of the tangents at the points
Therefore the angle (drawn roughly) at x = 0
this