Question

Let f(x)=x^3-7x^2+25x-39 and let g be the inverse function of f. What is the value of g'(0)?

Answer 1

Since f(3)=0, we know that g(0)=3.
The slope of the inverse function g is given by the formula

\[g'(x)=1/f'(g(x))\].

Thus,
\[g'(0)=1/f'(g(0))=1/f'(3)\].

Since \[f'(x)=3x^2-14x+25\], we know that \[f'(3)=3*3^2-14*3+25=10\].

Thus, \[g'(0)=1/10.\]

Answer 2

Thanks can you help with another?

Answer 3

Sure, if I'm able to help, I will. What's the question?