Search results
The equation of the tangent to y=f(x) at the point x=a is given by the formula: y=f'(a)(x-a)+f(a). The formula for the equation of tangent is derived from . The gradient of the tangent when is equal to the derivative at the point , which is given by .
- Contact Us
Learn maths at home Home; Book Online Tuition; Lessons;...
- Contact Us
In order to find the equation of a tangent line to a given function at a given point, you need to consider what a tangent line is.
- 5 min
- 152.3K
- Jake's Math Lessons
- Method
- Tips
Sketch the function and tangent line (recommended). A graph makes it easier to follow the problem and check whether the answer makes sense. Sketch the function on a piece of graph paper, using a graphing calculator as a reference if necessary. Sketch the tangent line going through the given point. (Remember, the tangent line runs through that point and has the same slope as the graph at that ...Take the first derivative to find the equation for the slope of the tangent line. [1] X Expert Source Jake Adams Academic Tutor & Test Prep Specialist Expert Interview. 20 May 2020. For function f(x), the first derivative f'(x) represents the equation for the slope of the tangent line at any point on f(x). There are many ways to take derivatives. Here's a simple example using the power rule ...Enter the x value of the point you're investigating. [3] X Expert Source Jake Adams Academic Tutor & Test Prep Specialist Expert Interview. 20 May 2020. Read the problem to discover the coordinates of the point for which you're finding the tangent line. Enter the x-coordinate of this point into f'(x). The output is the slope of the tangent line at this point. Example 1 (cont.): The point ...Write the tangent line equation in point-slope form. The point-slope form of a linear equation is y − y 1 = m ( x − x 1 ) {\displaystyle y-y_{1}=m(x-x_{1})} , where m is the slope and ( x 1 , y 1 ) {\displaystyle (x_{1},y_{1})} is a point on the line.[4] X Research source You now have all the information you need to write the tangent line's equation in this form. Example 1 (cont.): y − ...Confirm the equation on your graph. If you have a graphing calculator, graph the original function and the tangent line to check that you have the correct answer. If working on paper, refer to your earlier graph to make sure there are no glaring mistakes in your answer. Example 1 (cont.): The initial sketch showed that the slope of the tangent line was negative, and the y-intercept was well ...If necessary, start by rewriting the initial equation in standard form: f(x) = ... or y = ... Thanks Helpful 0 Not Helpful 0- 10 min
- 1.3M
- Jake Adams
Free tangent line calculator - find the equation of the tangent line given a point or the intercept step-by-step.
Jun 21, 2023 · Given a simple function \(y=f(x)\) and a point \(x\), be able to find the equation of the tangent line to the graph at that point. Graph both a function and its tangent line using a spreadsheet or your favorite software.
May 7, 2019 · In order to find the equation of the tangent line, you’ll need to plug that point into the original function, then substitute your answer for ???f(a)???. Next you’ll take the derivative of the function, plug the same point into the derivative and substitute your answer for ???f'(a)???.
People also ask
How do I find the equation of a tangent line?
How do you graph a tangent line?
How do you find the intersection of a tangent line?
How do you solve a tangent equation?
Where do you evaluate a tangent line?
How do you find the slope of a tangent?
Free tangent line calculator - step-by-step solutions to help find the equation of the tangent line to a given curve at a given point.
