About Graph slope calculator
Download Article Download Article Finding the Equation of a Tangent Line|Solving Related Problems|Video|Expert Q&A|Tips Unlike a straight line, a curve's slope constantly changes as you move along the graph. Calculus introduces students to the idea that each point on this graph could be described with a slope, or an "instantaneous rate of change." The tangent line is a straight line with that slope, passing through that exact point on the graph. To find the equation for the tangent, you'll need to know how to take the derivative of the original equation. 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 point.)Example 1: Sketch the graph of the parabola . Draw the tangent going through point (-6, -1).You don't know the tangent's equation yet, but you can already tell that its slope is negative, and that its y-intercept is negative (well below the parabola vertex with y value -5.5). If your final answer doesn't match these details, you'll know to check your work for mistakes.[1] 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:[2]Advertisement[3] 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 mentioned in the problem is (-6, -1). Use the x-coordinate -6 as the input for f'(x):f'(-6) = -6 + 3 = -3The slope of the tangent line is -3. The point-slope form of a linear equation is , where m is the slope and is a point on the line.[4] You now have all the information
Key features of the Graph slope calculator that are enabled through these drivers include:
- Graphing Calculators - Scientific Graphing Calculators
- Negative Slope Graph Calculator - Symbolab
- Slope Calculator: Graph Line and Find Properties
- Slope intercept form Calculator (y-intercept graph Calculator)
- Slope intercept form Calculator (y-intercept graph
- How To Use a TI Graphing Calculator to Find the Slope and the
- Slope Charts and Slope Graphs Charts for JavaScript
You need to write the tangent line's equation in this form. 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 below -5.5. The tangent line equation we found is y = -3x - 19 in slope-intercept form, meaning -3 is the slope and -19 is the y-intercept. Both of these attributes match the initial predictions. Here's a run-through of the whole process again. This time, the goal is to find the line tangent to at x = 2:AdvertisementFind the extreme points on a graph. These are points where the graph reaches a local maximum (a point higher than the points on either side), or local minimum (lower than the points on either side). The tangent line always has a slope of 0 at these points (a horizontal line), but a zero slope alone does not guarantee an extreme point. Here's how to find them:[5]Take the first derivative of the function to get f'(x), the equation for the tangent's slope.Solve for f'(x) = 0 to find possible extreme points.Take the second derivative to get f''(x), the equation that tells you how quickly the tangent's slope is changing.For each possible extreme point, plug the x-coordinate a into f''(x). If f''(a) is positive, there is a local minimum at a. If f''(a) is negative, there is a local maximum. If f''(a) is 0, there is an inflection point, not an extreme point.If there is a maximum or minimum at a, find f(a) to get the y-coordinate. The "normal" to a curve at a particular point passes through that point, but has a slope perpendicular to a tangent. To find the equation for the normal, take advantage of the fact that (slope of tangent)(slope of normal) = -1, when they both pass through the same point on the graph.[6] In other
