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Suppose a curve is defined by the function y = f(x) and you want the equation of the tangent at the point A.Suppose the x-coordinate at A is p. Then use y = f(p) to find the y-coordinate of A and let that be q. So, the point A is (p, q).
Next, find dy/dx, the derivative of the function f, with respect to q. This will be a constant or a functio of x. In the latter case, find its value for x = p. This is m, the gradient of the tangent.
So now you have the tangent line with gradient, m which passes through the point (p, q) and so its equation is
y - q = m(x - p)
Simplify this into the required form: y = mx + c or ax + by + c = 0.
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How do you get the tangent line without the graph?
The answer will depend on the context. If the curve in question is a differentiable function then the gradient of the tangent is given by the derivative of the function. The gradient of the tangent at a given point can be evaluated by substituting the coordinate of the point and the equation of the tangent, though that point, is then given by the point-slope equation.
What is the equation of the line tangent to the graph y equals sin 2x?
That line is [ y = 2 cos(2x) ].
How do you find the tangent of a circle?
a tangent is a line that touches the circle at only ONE point
How do you find gradient of a trend line?
Gradient is vertical rise / horizontal travel. If its derived from a mathematical expression, use differential calculus. If its a data driven ( hand drawn ) line, use best approximation tangent at point required.
Determine the point at which the graph of the function has a horizontal tangent line for the equation?
For the equation (9x^2)/(x^2+4)
How do you find the equation of a tangent line?
In order to find the equation of a tangent line you must take the derivative of the original equation and then find the points that it passes through.
Find the equation of a tangent line?
find the derivative to get the slope, then using the graph of the other line given to you, find a point on the graph that they share and plug it in to find the y-value. then use the point slope formulahttp://docs.google.com/gview?a=v&q=cache:P72siWJTFjwJ:gato-docs.its.txstate.edu/slac/Subject/Math/Calculus/Findting-the-Equation-of-a-Tangent-Line/Finding%2520the%2520Equation%2520of%2520a%2520Tangent%2520Line.pdf+how+to+find+the+equation+of+a+tangent+line&hl=en&gl=us&sig=AFQjCNFcYzt1d-PU9hE2gbQKngp4FeRw3Q
Find the equation of the line tangent to when x equals 8?
The question is suppose to read: Find the equation of the line tangent to y=(x²+3x)²(2x-2)³, when x=8
Why is calculus important in math?
calculus allows people to give numerical values to the slopes of curves and gives us a way to find things like to maximum value of a function that is too large to graph or find the equation of the tangent line to a curve at a certain point. Next to the general field of geometry, calculus has the most pratical applications to the real world
Derivative as the Slope of a Tangent?
Yes, the derivative of an equation is the slope of a line tangent to the graph.
Find an equation of the line tangent to the curve defined by x^2+3xy+y^4=32 at the point (2,2)?
55
What is an easy equation for finding the normal line?
The first thing you may want to do would be to find the tangent line to the function. The tangent line is a line that passes through a given point on a function, but does not touch any other point on the function (assuming the function is one to one). Assuming you have the tangent line, the normal line is simply perpendicular to the tangent line- it forms a 90 degree angle with the tangent line. One you have the tangent line and the point which it passes through, you can find the normal line. To obtain the perpendicular line to any function, take the inverse reciprocal of the slope (if your slope was 2, it is now -.5). After that, plug in your (x, y) coordinate, and you can solve for the constant b (assuming there is one). This should give the normal line to a tangent of at a point on a function.
How do you find the slope of the tangent line to each curve at the given point?
By differentiating the answer and plugging in the x value along the curve, you are finding the exact slope of the curve at that point. In effect, this would be the slope of the tangent line, as a tangent line only intersects another at one point. To find the equation of a tangent line to a curve, use the point slope form (y-y1)=m(x-x1), m being the slope. Use the differential to find the slope and use the point on the curve to plug in for (x1, y1).
How do you find a tangent line?
Say you are given a function and an x value.(1) First find the y coordinate that corresponds to that x value by plugging x into the function and simplifying to find y = some #. Now you have a point (x, y) that is not only on the function, but also on the tangent line.(2) Take the derivative of the function.(3) If the derivative still has xs in it, plug in the x value you were given and simplify. This should give you an actual number--the slope of the tangent line.(4) From steps 1 and 3, you now have a point on the tangent line and the slope of the tangent line. Use these two things to write the equation for the tangent line in y=mx+b form (m is the sope, plug in the point you found, solve for b, then rewrite the equation replacing m and b but leaving in x and y).
How do you get the tangent line without the graph?
The answer will depend on the context. If the curve in question is a differentiable function then the gradient of the tangent is given by the derivative of the function. The gradient of the tangent at a given point can be evaluated by substituting the coordinate of the point and the equation of the tangent, though that point, is then given by the point-slope equation.
What is the significance of the slope in the graphs?
This is the first fundemental theorem of Calculus. The slope of a line is very important in your first calculus course. The slope tells you the rate of change. This means how much is the object change in height compared to its change in length. The slope of a line in Calculus is used as the first derivative. If you can take the slope of a line at one particular point you will find the answer to the derivative at this point. Remember this. You first equation on your graph is called your position equation. If you take the derivative of this equation it is called the velocity equation. The velocity equation is how much the position equation is sloping at each point. If you take the derivative of the velocity equation you will get the acceleration equation. The accerelation equation is how much the velocity is sloping at each point. You can take the derivative of the acceleration equation and this will give you the jerk equation. The jerk equation is not used in many applications and I have never used this equation in any of my 4 calculus classes.
What is the equation of the line tangent to the graph y equals sin 2x?
That line is [ y = 2 cos(2x) ].
