Question

If f(x)=3x^2 -2x -3, let g(x)=f^-1(x). Find the slope of g(x)=f^-1(x) at the point (5,2).

a.) g'(5)=1/10
b.) g'(5)=1/5
c.) g'(5)=1
d.) g'(5)=2

I can't understand how to figure out this problem because I am unable to find a derivative for the function. How do I do this problem? Thank SO much!!

Answer 1

inverse of y = 3x^2 - 2x -3
-----> x = 3y^2 - 2y - 3
take derivative ...

1 = 6y dy/dx - 2dy/dx
1 = dy/dx(6y - 2)
dy/dx = 1/(6y-2)
at (5,2)
dy/dx = 1/(12-2) = 1/10