given that f(x) = x^5 +3x +6 is one to one, find (f^-1)' (10) (the derivative of the inverse function at x=10)
I know that the derivative of an inverse function = 1/f'(f^-1 (x))
f'(x) = 5x^4+3
However, I am not sure about how to find the value of f^-1 (10)
i know that point (10, y) on the inverse is the point (y, 10) on f(x)
So if I can isolate for the x value in the function f(x) = x^5 +3x +6 I will know (10, y) and I will know what f^-1 (10) is
however, f(x) is a quintic function, and I don't know how to isolate for the x value.
I've concluded there must be an easier way to solve this that I am not seeing, so any guidance would be much appreciated.
I know that the derivative of an inverse function = 1/f'(f^-1 (x))
f'(x) = 5x^4+3
However, I am not sure about how to find the value of f^-1 (10)
i know that point (10, y) on the inverse is the point (y, 10) on f(x)
So if I can isolate for the x value in the function f(x) = x^5 +3x +6 I will know (10, y) and I will know what f^-1 (10) is
however, f(x) is a quintic function, and I don't know how to isolate for the x value.
I've concluded there must be an easier way to solve this that I am not seeing, so any guidance would be much appreciated.