question_answer

The numbers P, Q and R for which the function \[f\left( x \right)=P{{e}^{2x}}+Q{{e}^{x}}+Rx\] satisfies the conditions \[f\left( 0 \right)=-1,\]  \[f'\,\,(log\,\,2)=31\] and \[\int_{0}^{\log 4}{[f(x)-Rx]\,\,dx=\frac{39}{2}}\]  are given by

A)  \[P=2,\,\,Q=-3,\,\,R=4\]

B)  \[P=-5,\,\,Q=2,\,\,R=3\]

C)  \[P=5,\,\,Q=-2,\,\,R=3\]

D)  \[P=5,\,\,Q=-6,\,\,R=3\]

E)  None of these