Let , where and are constants. The function satisfies . Determine the values of and…

MATHEMATICS · Subjective · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

Let

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

, where

k

and

m

are constants. The function satisfies

f(1)=\dfrac{11}{3},\quad (f^{-1})'\!\left(\dfrac{11}{3}\right)=\dfrac{1}{5},\quad\text{and}\quad (f^{-1})'(0)=\dfrac{1}{3}

. Determine the values of

k

and

m

.

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