# calculus

Show that the tanget lines to the graph of Y= e^x - e^-x /e^x + e^-x at x =1 and x= -1 are parallel.
I know to use the Quotient rule but I am having a hard time with this problem.

1. 👍 0
2. 👎 0
3. 👁 47
1. y = tanh(x)
there are asymptotes at y=1 and y=-1

just consider when x gets large positive. e^-x vanishes, and you have e^x/e^x = 1

when x gets large negative, e^x vanishes, and you have -e^-x/e^-1 = -1

1. 👍 0
2. 👎 0
posted by Steve
2. first of all simplify it a bit,
multiplying top and bottom by e^x to get
y = (e^(2x) -1)/(e^(2x) + 1)

dy/dx = [(e^(2x) + 1)(2e^(2x)) - (e^(2x) -1)(2e^(2x)) )/(e^(2x) + 1)^2
= 2e^(2x)(e^(2x) + 1 + e^(2x) - 1)/(e^(2x+1)^2
= 4e^(2x)/(e^(2x)+1)^2

confirmed by Wolfram:
http://www.wolframalpha.com/input/?i=derivative+of+%28e^x+-+e^-x%29%2F%28e^x+%2B+e^-x%29

I will leave it up to you to sub in x=1 and x=-1 to show that you get the same value, I did.

1. 👍 0
2. 👎 0
posted by Reiny
3. thank you very Much

1. 👍 0
2. 👎 0
posted by dino

## Similar Questions

1. ### calculus

find one point on the graph of y= x+2cosx such that the tanget is horizontal

asked by kenisha on August 6, 2012
2. ### math

how to graph this y=6x+20 Graph the y-intercept. Show the lines that indicate the use of slope to graph two more points Draw the line representing the graph of the equation

3. ### Technology

When using a line graph, why is it inportant to only graph 1 - 3 series of data? A line graph in Microsoft Excel will not allow you to graph more than 3 series of data. It will not show changes over time of you use more than 3

asked by Estephania on January 18, 2016
4. ### Calculus

The graph of the equation x2 − xy + y2 = 9 is an ellipse. Find the lines tangent to this curve at the two points where it intersects the x-axis. Show that these lines are parallel.

asked by Al on October 26, 2014
5. ### college algebra

Question 638522: Graph the following function using transformations. Be sure to graph all of the stages on one graph. State the domain and range. For example, if you were asked to graph y= x^2+ 1 using transformations, you would

asked by beatrize on December 11, 2012
6. ### college algebra

Graph the following function using transformations.  Be sure to graph all of the stages on one graph.  State the domain and range.    For example, if you were asked to graph  y= x^2+11 using transformations, you would

asked by beatrize on December 11, 2012
7. ### biology

1. Which sentence from the section "Line Graphs" BEST introduces when to use a line graph to display information to the reader? A line graph uses dots connected by lines to show how amounts change over time. A dot over each month

asked by person on January 22, 2018
8. ### math, help

can someone show me how to do this one i have plenty of them so can you show me step by step when someone gets a chance. Thank you. Solve the system by graphing x+y=3 x+y=-1 What I would do is to put the equations in slope

asked by jasmine20 on February 10, 2007
9. ### cal

Equations of the tangent lines to hyperbola xy=1 that pass through point (-1,1) I know the graph of y=1/x but not sure about the tangent lines at given point. Are the lines tangent to (1,1) and (-1,-1)? You're correct, the graph

asked by Melba on September 26, 2006
10. ### pre calculus

2. Graph the following function using transformations. Be sure to graph all of the stages on one graph. State the domain and range. y= -2 lxl +2 For example, if you were asked to graph y= x^2 + 1 using transformations, you would

asked by michelle on April 2, 2013

More Similar Questions