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

Using a number strip substract , Another aid that can help children pract...

Another aid that can help children practise subtraction is the number strip. TGS can be used to improve their ability to count backwards. For example, subtracting 4 from 9 means

Simple derivatives, Simple derivatives Example   Differentiate followin...

Simple derivatives Example   Differentiate following.  (5x 3   - 7 x + 1) 5 ,[ f ( x )] 5 ,[ y ( x )] 5 Solution: Here , with the first function we're being asked to

Calculate subsequent proportion, Calculate subsequent proportion: A re...

Calculate subsequent proportion: A recipe calls for 1(1/2) cups of flour to make servings for 6 people.  How much flour should be used to make servings for 4 people? Solut

Find the maxima or minima and green theorem, 1) find the maxima and minima ...

1) find the maxima and minima of f(x,y,z) = 2x + y -3z subject to the constraint 2x^2+y^2+2z^2=1 2)compute the work done by the force field F(x,y,z) = x^2I + y j +y k in moving

Prove that a tree with n vertices has n - 1 edges, Prove that A tree with n...

Prove that A tree with n vertices has (n - 1) edges.    Ans: From the definition of a tree a root comprise indegree zero and all other nodes comprise indegree one. There should

Evaluate following. 0ln (1+)excos(1-ex)dx substitution, Evaluate following....

Evaluate following. ∫ 0 ln (1 + π )   e x cos(1-e x )dx Solution The limits are little unusual in this case, however that will happen sometimes therefore don't get

Trignometry, prove that cos(a)/1-sin(a)=tan(45+A/2)

prove that cos(a)/1-sin(a)=tan(45+A/2)

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