Question

For the function $f\left(x\right)=1+3^x\log 3$, the antiderivative $F$ assume the value $7$ for $x=2$. At what value of $x$ does the curve $y=F\left(x\right)$ cut the abscissa?

• A. $x=3$
• B. $x=1$
• C. $x=0$
• D. None of these

Answer 1

The correct option is B $x=1$

$f\left(x\right)=1+3^x\log 3\therefore F\left(x\right)=\int (1+3^x\log 3)dx=x+3^x+c$
Since $F\left(2\right)=2+9+c=7\Rightarrow c=-4$
$\therefore F\left(x\right)=x+3^x-4=0\Rightarrow x=1$