For (x>0 ), let (F(x)=x^ 2 k(x) ) and (F'(x)=x^ 2 x+4x ). If (k(1)=3 ), which of the…

MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

For

x>0

, let

F(x)=x^{2}k(x)

and

F'(x)=x^{2}\ln x+4x

. If

k(1)=3

, which of the following is

k(x)

? (a)

\dfrac{x}{3}\ln x+\dfrac{x}{9}+2+\dfrac{10}{9x^{2}}

(b)

\ln x+\dfrac{4}{x}

(c)

\dfrac{x}{3}\ln x-\dfrac{x}{9}+2+\dfrac{10}{9x^{2}}

(d)

\dfrac{x}{3}\ln x-\dfrac{x}{9}+\dfrac{28}{9}

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