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

Stratified sampling, Stratified sampling In stratified sampling case t...

Stratified sampling In stratified sampling case the population is divided into groups in such a way that units in each group are as same as possible in a process called strati

Linear equations, Linear Equations - Resolving and identifying linear fir...

Linear Equations - Resolving and identifying linear first order differential equations. Separable Equations - Resolving and identifying separable first order differential

Write down the first few terms of the sequences, Write down the first few t...

Write down the first few terms of each of the subsequent sequences. 1. {n+1 / n 2 } ∞ n=1 2. {(-1)n+1 / 2n} ∞ n=0 3. {bn} ∞ n=1, where bn = nth digit of ? So

The distributive law, The Distributive Law :  If you were asked to mentall...

The Distributive Law :  If you were asked to mentally multiply 37 with 9, how would you proceed? 1 would do it as follows - 37 is 30 + 7, 30 x 9 = 270, 7 x 9 = 63, so 270 + 63, th

Introduction To Numerical Methods & Matlab, Can you help me with the course...

Can you help me with the coursework i have in Matlab?

MUTIPLYING FRACTIONS, EVERY TIME I TRY TO DO ANY KIND OF FRACTIONS WELL MUL...

EVERY TIME I TRY TO DO ANY KIND OF FRACTIONS WELL MULTIPLYING I ALWAYS GET IT WRONG

Find the length of the second diagonal, Find the length of the second diago...

Find the length of the second diagonal of a rhombus, whose side is 5cm and one of the diagonals is 6cm.

Statistics, what is the meaning of statistics

what is the meaning of statistics

Defining real numbers, The numbers used to measure quantities such as lengt...

The numbers used to measure quantities such as length, area, volume, body temperature, GNP, growth rate etc. are called real numbers. Another definition of real numbers us

Rate and ratio, express 4:24 as fraction in lowest term

express 4:24 as fraction in lowest term

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