csat-suneung 2018 Q11

csat-suneung · South-Korea · csat__math-science 3 marks Composite & Inverse Functions Derivative of an Inverse Function

There are two functions $f ( x ) , g ( x )$ differentiable on the set of all real numbers. $f ( x )$ is the inverse function of $g ( x )$ and $f ( 1 ) = 2 , f ^ { \prime } ( 1 ) = 3$. If the function $h ( x ) = x g ( x )$, what is the value of $h ^ { \prime } ( 2 )$? [3 points]
(1) 1
(2) $\frac { 4 } { 3 }$
(3) $\frac { 5 } { 3 }$
(4) 2
(5) $\frac { 7 } { 3 }$

There are two functions $f ( x ) , g ( x )$ differentiable on the set of all real numbers. $f ( x )$ is the inverse function of $g ( x )$ and $f ( 1 ) = 2 , f ^ { \prime } ( 1 ) = 3$. If the function $h ( x ) = x g ( x )$, what is the value of $h ^ { \prime } ( 2 )$? [3 points]\\
(1) 1\\
(2) $\frac { 4 } { 3 }$\\
(3) $\frac { 5 } { 3 }$\\
(4) 2\\
(5) $\frac { 7 } { 3 }$

Paper Questions

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