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How do you find the x and y coordinates of all points on the graph of f where the line tangent to the graph is parallel to the x-axis?
"Parallel to the x-axis" is the same as saying "a slope of zero".
In calculus, you take the derivative of f and make it equal to zero. Then solve the equation.
Taking a simple case, consider the equation f(x) = 2x2 -5x -4
To find all the places that the graph is parallel to the x-axis, take the derivative
4x - 5
and make that equal zero
4x - 5 = 0
Then solve for x. The only point where is graph is parallel to the x axis is where x=5/4. Put that back in the original equation and get the y coordinate for that point.
This class of problems makes you use a great variety of skills. All of your first year calculus will depend on your ability to thoroughly understand this and similar processes.
What else can I help you with?
How do you graph a parallel line?
You need to know what the graph points are.
What are pairs of numbers that show points on a graph?
Coordinates.
How do you get the slope of a line on a graph?
Take a tangent at the point where you want the slope. Then the slope of the graph at that point is the slope of the tangent, which is found by taking another point on the tangent and then taking the change in y between the two points and divid it by the change in x.
What is a tangent line?
Tangent line is a graph. This graph is to gather data.
How are the graph of an equation and the set of all solutions of an equation related?
The coordinates of every point on the graph, and no other points, are solutions of the equation.
How do you graph a parallel line?
You need to know what the graph points are.
What are pairs of numbers that show points on a graph?
Coordinates.
How do you draw a scatter graph?
Plot points on Cartesian coordinates.
What is it called to have two different coordinates on a graph but have the same slope?
I believe they are parallel.
How do you get the slope of a line on a graph?
Take a tangent at the point where you want the slope. Then the slope of the graph at that point is the slope of the tangent, which is found by taking another point on the tangent and then taking the change in y between the two points and divid it by the change in x.
How can one determine the distance between two points on a graph using the keyword "how to find distance on a graph"?
To determine the distance between two points on a graph, you can use the distance formula, which is derived from the Pythagorean theorem. This formula calculates the distance as the square root of the sum of the squares of the differences in the x-coordinates and y-coordinates of the two points. By plugging in the coordinates of the two points into the formula, you can find the distance between them on the graph.
What is a tangent line?
Tangent line is a graph. This graph is to gather data.
What is true about all coordinate points in quadrant IV of a coordinate graph?
Their first coordinates are positive and their second coordinates are negative.
Why do you need coordinates?
They are used to map points on a graph and are used to make real maps as well as graph probabilities and distances.
How are the graph of an equation and the set of all solutions of an equation related?
The coordinates of every point on the graph, and no other points, are solutions of the equation.
What is the graph of a line with a slope one half that contains the points -6 and 6?
' -6 ' and ' 6 ' are not points. On a 2-dimensional (flat) graph, you need two coordinates to locate one point. (On a 3-dimensional (solid) graph, you need three coordinates to locate one point. And there's no such thing as a 1-dimensional graph.)
The set of points whose coordinates satisfy an equation is called what the of the equation?
Just took the vocab test the answer is graph.
