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

Find out the surface area of the solid - parametric curve, Find out the sur...

Find out the surface area of the solid acquired by rotating the following parametric curve about the x-axis. x = cos 3 θ y = sin 3 θ  0 ≤ θ ≤ ?/2 Solution We wil

Permutations and Combinations, How many 4 digit number lass than 6000 can b...

How many 4 digit number lass than 6000 can be made with the digits 7,6,4 and 2 if digits are not repeated?

Permuation and combination, how many words can be formed from letters of wo...

how many words can be formed from letters of word daughter such that word contain 2vowles and 3consonant

Properties of dot product - vector, Properties of Dot Product u → • (v...

Properties of Dot Product u → • (v → + w → ) = u → • v → + u → • w →          (cv → ) • w → = v → •(cw → ) = c (v → •w → ) v → • w → = w → • v →

Word problems, A baseball card was worth $5.00 in 1940. It doubled in value...

A baseball card was worth $5.00 in 1940. It doubled in value every decade. How much was it worth in 2000?

Determinants, can anyone solve this assigment: D=lsqrt(3x-5) sqrt(2x)l ...

can anyone solve this assigment: D=lsqrt(3x-5) sqrt(2x)l =3 l -1 1 l

Find the tangent to the curve, 1. Find the third and fourth derivatives of ...

1. Find the third and fourth derivatives of the function Y=5x 7 +3x-6-17x -3 2. Find the Tangent to the curve Y= 5x 3 +2x-1 At the point where x = 2.

If t2+t+1=0 , t=w,w 2 L.H.S (w+w 2 ) + (w 2 + w) 2 ........  1  + 1 ....

t=w,w 2 L.H.S (w+w 2 ) + (w 2 + w) 2 ........  1  + 1 ..... But every third term is of the form: (w 3n +w 3n ) 2 =22 There are nine such terms. Their sum is 36. The rema

Problem Solving, the low temperature in anchorage alaska today was negative...

the low temperature in anchorage alaska today was negative four degrees what is the difference in the two low temperatures

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