What is y=x+2 graphed
1 answer:
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Answer:
a)
x = -1/√3 = -0.58 is a local maximum
x = 1/√3 = 0.58 is a local minimum
b)
(-1/√3 , 1/√3 ) DECREASING
(-∞, -1/√3) U (1/√3, ∞) INCREASING
Step-by-step explanation:
To answer all of the questions we must obtain the derivative of the fucntion:
If
U(x) = 4(x^3 - x)
then
U'(x) = 4(3x^2 - 1)
U''(x) = 4(3*2 x) = 24 x
U'''(x) = 24
The local maxima and minima of the function U(x) can be found when U'(x) = 0
this occurs when :
3x^2 = 1
that is:
x = ±1/√3
We will know if they are a minimum or a maximum evaluating this points on the second derivative (you can look for it as <u><em>Second derivative test</em></u>), if the result is positive the point corresponds to a minimum and if it is negative it will be a maximum.
Here it is easy to determine wheather is a maximum or a minimum because the second derivative is 24x, therefore if x is negative or positive so the second derivative will be.
a)
x = -1/√3 = -0.58 is a local maximum
x = 1/√3 = 0.58 is a local minimum
b)
the intervals at which the function is increasing { decreasing } is given when the first derivative is positive { negative }
The first derivative will be positive when:
3x^2 > 1
|x| > 1/√3 --> x > 1/√3 and x < -1/√3
The first derivatice will be negative when:
3x^2 < 1
|x| < 1/√3 --> x < 1/√3 and x > -1/√3
Therefore the intervals are:
(-1/√3 , 1/√3 ) DECREASING
(-∞, -1/√3) U (1/√3, ∞) INCREASING
<u><em>** The attached image is a plot of the fucntion where you can see part of the intervals and the local maximum and minimum</em></u>
This is probably asking you to consider the symmetry of f(x). If f(x) is equal to f(-x), then f is symmetric about the origin. If f(x) is equal to -f(x), then f is symmetric about the y-axis.
Answer:
T F F F T F T
Step-by-step explanation:
A 2D vector can have a component equal to zero even when its magnitude is nonzero. TRUE.
it will be actually a 1d vector, but it's still a 2d vector too. this happens when the vector it's aligned to one of the axis.
The direction of a vector can be different in different coordinate systems. FALSE
The direction of a vector is independent of any coordinate system.
A 2D vector can have a magnitude equal to zero even when one of its components it nonzero. FALSE.
because the only way is that both x and y are equal to zero
The magnitude of a vector can be different in different coordinate systems. FALSE.
The magnitude stays the same in every coordinate system
It is possible to multiply a vector by a scalar. TRUE.
it changes only it's magnitude.
It is possible to add a scalar to a vector. FALSE.
you can´t sum elements of diferent spaces. R, , etc
The components of a vector can be different in different coordinate systems.TRUE.
The components of a vector are just a way for identifying the vector, in a determinate coordinate system, the way i call those components will change as I change the name I call every point in the plane.