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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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)Quote:
Originally Posted by sandra17
so we want a solution to
f(x)=7
x^3 - (x/2)=7
x=2 works
so
f^(-1)(7)=2
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now find f'(x)
f'(x)=3x^2-1/2
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finally
(f^-1)^' (7)=1/[f'(f^(-1)(7))]
=1/[f'(2)]=1/(3(2)^2-1/2)=1/(23/2)=2/23