Question

At what point of the curve of y = coshx does the tangent have slope 1

Answer 1

Answer:

Step-by-step explanation:

slope =1

dy/dx=1

d/dx ( cos hx ) =1

d/dx (e^x+e^-x /2 ) =1

1/2 d/dx ( e^x+e^-x)=1

1/2(e^x-e^-x) =1

e^x-e^-x=2

e^x-1/e^x =2

e^2x-1=e^x

e^x=t

t^2-1=t

t^2-t-1=0

t=1 plus or minus root (1+4 ) /2

t=1 plus or minus root 5  /2

e^x = 1 plus or minus root 5  /2

take ln on both sides

x=ln  ( 1 plus or minus root 5  /2  )