Question

Calculus help please?

Answer 1

@KendrickLamar2014 @TheSmartOne

Answer 2

@ParthKohli

Answer 3

@Vocaloid

Answer 4

@jabez177

Answer 5

\[\frac{ d }{ dx }\left( f^{-1}(x) \right)=\frac{ 1 }{ f'(f^{-1}(x)) }\]

f(x) is decreasing on a < x < b, so f'(x) < 0.
I'm thinking that means the derivative of the inverse is negative as well, but I'm not sure on that

Answer 6

Think of this: d/dx (f(x) is slope of the line, you can find it out by using formula (y_2-y_1)/(x_2-x_1).
Theb f^(-1) (x) is inverse of f(x) that means the line of f^(-1) perpendicular to line f(x) , hence, slope of it is =-1/slope of the first line.