Tangent Slope at Point y=\cosh x = 1

  • Thread starter bard
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In summary, the tangent slope at the point y=cosh x=1 is equal to 0 and can be calculated using the derivative of the function y=cosh x=1. It represents the rate of change of the function and is constant and positive for all values of x. It can never be negative due to the increasing nature of the function.
  • #1
bard
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at what point on the curve [tex]y=\cosh x[/tex] does the tangent have slope 1


I have no idea how to approach this problem

my work

[tex]1=\sinh x\frac{dy}{dx}[/tex]

[tex]\frac{1}{sinh x}=\frac{dy}{dx}[/tex]
 
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  • #2
It would probably help to you use the definitions.

For example:
[tex]\sinh{x}= \frac{e^{x}-e^{-x}}{2}[/tex]
 
  • #3
yah I found the answer as x=ln[1+sqt2]----thanks for your help
 

1. What is the tangent slope at the point y=cosh x=1?

The tangent slope at the point y=cosh x=1 is equal to 0. This is because the function y=cosh x=1 has a horizontal slope at x=0, meaning that the slope of the curve at this point is 0.

2. How is the tangent slope at the point y=cosh x=1 calculated?

The tangent slope at the point y=cosh x=1 can be calculated using the derivative of the function y=cosh x=1. The derivative of cosh x is sinh x, and when x=0, sinh x=0, hence the slope at this point is 0.

3. What does the tangent slope at the point y=cosh x=1 represent?

The tangent slope at the point y=cosh x=1 represents the rate of change of the function y=cosh x with respect to x at x=0. It indicates the steepness of the curve at this particular point.

4. Is the tangent slope at the point y=cosh x=1 constant?

Yes, the tangent slope at the point y=cosh x=1 is constant. This is because the function y=cosh x=1 is symmetric about the y-axis, and therefore, the slope of the curve at x=0 will remain the same for all values of x.

5. Can the tangent slope at the point y=cosh x=1 ever be negative?

No, the tangent slope at the point y=cosh x=1 can never be negative. This is because the function y=cosh x=1 is always increasing and the slope at x=0 is 0, meaning that the slope will always be positive for all values of x.

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