f(x) = x^5 + 3x^3 + 2x - 1; P(5,1)

a) Use f' to prove that f has an inverse function
b) Find the slope of the tangent line at the point P on the graph of f-1

Question

f(x) = x^5 + 3x^3 + 2x - 1;  P(5,1)

a) Use f' to prove that f has an inverse function
b) Find the slope of the tangent line at the point P on the graph of f-1

bahrom7893 · Answer

http://en.wikipedia.org/wiki/Inverse_functions_and_differentiation According to that $$\frac{dx}{dy}*\frac{dy}{dx}=1$$Find both of those.

bahrom7893 · Answer

$$y = x^5 + 3x^3 + 2x - 1$$$$\frac{dy}{dx}=5x^4+9x^2+2$$

bahrom7893 · Answer

Now use implicit differentiation again to find $$\frac{dx}{dy}$$

anonymous · Answer

ok, so Dy/dx is increasing, so it's on-to-one, and therefore a function!  but I don't even know how to find the slope per the question...I appreciate your time here!

bahrom7893 · Answer

You need to find $$\frac{dx}{dy}$$which should be easy to find via implicit differentiation.. For some reason I'm blanking on that right now. Once you find dx/dy, you can just plug in your point and get the slope.

anonymous · Answer

ok. thanks, I think I can take it from here.

anonymous · Answer

Implicit  differentiation is not one of my strong point,,guess this is a good time to review!