# compute the tangent line

• June 6th 2007, 10:47 AM
viet
compute the tangent line
need help with this one:

Quote:

compute the tangent line of the graph of $f(x) = 3+2sinhx$ at $x = 0$.
Use the inverse function slope relation to find the corresponding tangent line of the graph of $g = f^{-1}$
• June 6th 2007, 02:24 PM
Rebesques
Well, we know that the tangent line will pass through (0,f(0)) and have slope of f'(0). Just write down y=ax+b and use these two conditions to obtain a,b.

(hint: a=f'(0) straight away)

For the tangent to the inverse function, it will pass through the point (f(0),0) and have a slope of 1/f'(0). Use the same argument here also.