If $F\left(x\right)=f\left(x\right)g\left(x\right)h\left(x\right)$ for all real $x$, where $f\left(x\right),g\left(x\right)$and $h\left(x\right)$ are differentiable functions at some point $x_0$If  $F^{|}\left(x_0\right)=21F\left(x_0\right),f^{|}\left(x_0\right)=4f\left(x_0\right),g^{|}\left(x_0\right)=-7g\left(x_0\right)$  and  $h\text{'}\left(x_0\right)=kh\left(x_0\right)$, then $k=$

$F\left(x\right)=f\left(x\right)g\left(x\right)h\left(x\right)\forall x\in R$

$F^{|}\left(x\right)=f^1\left(x\right)g\left(x\right)h\left(x\right)+f\left(x\right)g^{|}\left(x\right)h\left(x\right)+f\left(x\right)g\left(x\right)h^{|}\left(x\right)$

$\text{at\hspace{0.17em}\hspace{0.17em}}x=x_0$

$F^{|}\left(x_0\right)=f^1\left(x_0\right)g\left(x_0\right)h\left(x_0\right)+f\left(x_0\right)g^{|}\left(x_0\right)h\left(x_0\right)+f\left(x_0\right)g\left(x_0\right)h^{|}\left(x_0\right)$

$21F\left(x_0\right)=4f\left(x_0\right).g\left(x_0\right)h\left(x_0\right)-7f\left(x_0\right)g\left(x_0\right)h\left(x_0\right)+k.h\left(x_0\right)f\left(x_0\right)g\left(x_0\right)$

$21=4-7+k[\because F\left(x_0\right)=f\left(x_0\right).g\left(x_0\right)h\left(x_0\right)]$

$\Rightarrow k=24$