Mathematics

Mathematics

Problem

Let

f

be a differentiable function defined by

f(x)=k x^{3}+2

, where

k

is a non-zero constant. The inverse function

f^{-1}

exists for the relevant values of

x

and

y

, and it is known that

(f^{-1})'(10)=\dfrac1{24}

. Determine the value of the constant

k

. Show all reasoning. a. Calculate the value of

k

.

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