please show all steps for the following problem Find (f^-1)^' (7) for the function f(x) = x^3 - (x/2), x > 0 any help would be appreciated
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Originally Posted by sandra17 please show all steps for the following problem Find (f^-1)^' (7) for the function f(x) = x^3 - (x/2), x > 0 any help would be appreciated first we need to find f^(-1)(7) so we want a solution to f(x)=7 x^3 - (x/2)=7 x=2 works so f^(-1)(7)=2 ----- now find f'(x) f'(x)=3x^2-1/2 ---- finally (f^-1)^' (7)=1/[f'(f^(-1)(7))] =1/[f'(2)]=1/(3(2)^2-1/2)=1/(23/2)=2/23
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