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How do you find the coordinates of the stationary point on the graph of y equals x root(x plus 1)?
Wiki User
∙ 6y ago
A stationary point is where the derivative of a function is equal to zero. Let's find it for f(x)= x(x+1)^.5. Using the product rule and power rule, we compute f'(x)=x(.5)(x+1)^-.5+(x+1)^.5=[x(.5)+(x+1)]/[(x+1)^.5]. We now set this equal to zero. We can now ignore the denominator because as long as the numerator equals zero and the denominator does not equal zero, the whole thing equals zero. So 0=x(.5)+(x+1)=.5x+x+1=1.5x+1-->1.5x=-1-->x=-1/1.5=-2/3. Note that x=-2/3 does not make the denominator zero, so we have found the only stationary point. Note that f(-2/3)=(-2/3)(-2/3+1)^.5=(-2/3)(1/3)^.5≈-0.3849. That's it.
Wiki User
∙ 6y ago
Wiki User
∙ 6y agoy = x*sqrt(x + 1)dy/dx = sqrt(x + 1) + x*1/2*1/sqrt(x + 1)
dy/dx = 0 => sqrt(x + 1) + x*1/2*1/sqrt(x + 1) = 0
sqrt(x + 1) = - x*1/2*1/sqrt(x + 1)
Multiplying both sides by sqrt(x + 1) [it can be shown that sqrt(x + 1) is not 0 at the turning point.]
(x + 1) = -x/2 or 2x + 2 = -x => 3x = -2 or x = -3/2.
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What does to graph a point mean?
Mark the position of the point on the graph according to the coordinates of the point that are given (or calculated).
What is the lowest point of y equals x squared?
If you mean the graph, then the lowest coordinates would be (0,0). Also known as the origin.
What does it mean on a graph when x equals 0?
When x = 0, the point that has (0, y) coordinates will be on the y-axis for any y.
A pair of numbers used to determine the posittion of a point on a graph?
coordinates
What are the 2 numbers that tel you the exact location on the graph called?
In a euclidean graph, the position of a point on the graph is denoted by its Coordinates (x,y).
What does to graph a point mean?
Mark the position of the point on the graph according to the coordinates of the point that are given (or calculated).
What is the lowest point of y equals x squared?
If you mean the graph, then the lowest coordinates would be (0,0). Also known as the origin.
What does it mean on a graph when x equals 0?
When x = 0, the point that has (0, y) coordinates will be on the y-axis for any y.
For every point on the graph of Fx Is there is a point on the graph of F-1y with reversed coordinates?
False
What is the highest point on a graph?
The highest point on a graph is when the derivative of the graph equals 0 or the slope is constant.
A pair of numbers used to determine the posittion of a point on a graph?
coordinates
What is the coordinates for y equals x y equals -x plus 2?
The coordinates of the point of intersection is (1,1).
What are the 2 numbers that tel you the exact location on the graph called?
In a euclidean graph, the position of a point on the graph is denoted by its Coordinates (x,y).
What are two numbers that describe the location of a point on a graph?
The number are called coordinates.
What is the point called that crosser the x and y axis on the graph?
It is the point of origin and its coordinates are at (0, 0)
Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is even?
If the point (x,y) is on the graph of the even function y = f(x) then so is (-x,y)
How do you determine where to mark a point on the graph?
At the given coordinates where the x and y values intersect
