Given that g is the inverse function of f, and f(3)=4, and f'(3)=5, then g'(4)= ?
To find g'(4), we can use the inverse function theorem. According to the inverse function theorem, if g is the inverse function of f and f'(x) exists and is non-zero at a point c, then g'(f(c)) = 1 / f'(c).
In this case, we are given that g is the inverse function of f and f(3) = 4. We are also given that f'(3) = 5.
To find g'(4), we need to find g'(f(3)). Since f(3) = 4, we want to find g'(4).
Using the inverse function theorem, we have:
g'(4) = 1 / f'(3)
Since f'(3) = 5, we can substitute this value in the equation:
g'(4) = 1 / 5
Therefore, g'(4) = 1/5.