Tangent lines, Mathematics

Assignment Help:

Tangent Lines : The first problem which we're going to study is the tangent line problem.  Before getting into this problem probably it would be best to define a tangent line.

A tangent line to the function f(x) at the instance x = a is a line which just touches the graph of the function at the point in question & is "parallel" (in some way) to the graph at that point. Consider the  graph below.

1835_common graph 11.png

In this graph the line is a tangent line at the specified point because just it touches the graph at that point and is also "parallel" to the graph at that point.  Similarly, at the second point illustrated, the line does just touch the graph at that point, hence it is not "parallel" to the graph at that point & hence it's not a tangent line to the graph at that point.

At the second point illustrated (the point where the line isn't a tangent line) we will sometimes call the line a secant line.

Now, we've used the word parallel a couple of times and we have to probably be a little careful with it.  Generally we will think of a line & a graph as being parallel at a point if they are both moving in the same direction at that point. So, in the first point above the graph and the line are moving in the same direction and so we will say they are parallel at that point.  At the second point, on the other hand, the line and the graph are not moving in the same direction and so they aren't parallel at that point.


Related Discussions:- Tangent lines

First and second order derivative, Solution : We'll require the first and s...

Solution : We'll require the first and second derivative to do that. y'(x) = -3/2x -5/2                                     y''(x) = 15/4x -7/2 Plug these and also the funct

Subtract, Ask question Minimum 100 words accepted# 1000-101

Ask question Minimum 100 words accepted# 1000-101

Matric, fgdg ggghfr hhrhfrf hfrrg jhj hjgg dear friend ghr tu vgu jyyiu ui ...

fgdg ggghfr hhrhfrf hfrrg jhj hjgg dear friend ghr tu vgu jyyiu ui u huik bgyuiiyts husk

Derivative with polar coordinates - parametric equations, Derivative with P...

Derivative with Polar Coordinates dy/dx = (dr/dθ (sin θ) + r cos θ) / (dr/dθ (cosθ) - r sinθ) Note: Rather than trying to keep in mind this formula it would possibly be easi

Shares and dividends, how to see shares and dividends of a company and are ...

how to see shares and dividends of a company and are they seen day wise?

Marketing, What are the Input and Output of Marketing

What are the Input and Output of Marketing

Minimizes the sum of the two distance, The value of y that minimizes the su...

The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as a/b where a and b are coprime positive integers. Find a+b.

Elli[ital paths of celestial bodies, Create a detailed diagram to describe ...

Create a detailed diagram to describe the equation of an ellipse in terms of it’s eccentricity and indicate how the foci and major and minor semi-axes are involved. Y

Space geometry, a sketch of two dimensional system

a sketch of two dimensional system

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd