carter

Question

suppose f(x) = (4/5)x^2 + cosx for x≥0 and g is the inverse of f. find g'(1.5) to the nearest thousandth.

would I just swap x and y and then find the derivative of that equation to find g'(x) and then plug in g'(1.5)? When I swapped x and y I got x=(4/5)y^2 + cosy and then do I do implicit differentiation? I at implicit differentiation so I'm stuck already :(

(i posted it incorrectly before my bad)

Answer 1

did it work?
See your previous post for a clue, and read up on inverse function derivatives.

Answer 2

I read your hint and I'm still confused on how to approach the problem. Am I supposed to find the derivative of f(x), and then do 1/f'(x) with the x being 1.5 to find g'(x)?

Answer 3

find x such that f(x) = 1.5
I get f(1.18) = 1.5
so g'(1.5) = 1/f'(1.18)

Answer 4

I tried solving f(x) = 1.5 and I get 0=(4/5)x^2 + cosx - 1.5
How did you get 1.18 from there?