How to modify the direction of this arrow?

I think plain TikZ is not so difficult as OP complained ^^ What does plain mean? SIMPLE! Change [yscale=.8,xscale=1.4] as you wish!

\documentclass[tikz,border=5mm]{standalone}
\begin{document}
\begin{tikzpicture}[yscale=.8,xscale=1.4]
\draw[shift={(-.5,.5)}] (0,0) rectangle +(8,-5) 
(0,-1)--+(0:8) (0,-2)--+(0:8) (1,0)--+(-90:5);
\path
(0,0)    node{$x$}          % <<< line 1
++(0:1)  node{$0$}
++(0:2)  node{$\alpha -1$}
++(0:2)  node{$x^*(\alpha)$}
++(0:2)  node{$+\infty$}
(0,-1)   node{$f'_{\alpha}(x)$}         % <<< line 2
++(0:2)  node{$+$}
++(0:1)  node{$0$}
++(0:1)  node{$-$}
++(0:2)  node{$-$}
(0,-3)   node{$f_{\alpha}(x)$}          % <<< line 3
++(0:1)  node (A) {$0$}
++(0:2)  +(90:1) node (B) {$f_{\alpha}(\alpha -1)$}
++(0:2)  node (C) {$0$}
++(0:2)  +(-90:1) node (D) {$-\infty$}
;
\foreach \p/\q in {A/B,B/C,C/D}
\draw[-stealth,magenta] (\p)--(\q);
\end{tikzpicture}
\end{document}

I used the intermediate tab value command from page 33 of the manual

\tkzTabVal{2}{3}{0.5}{$x^*(\alpha)$}{0}

the {2}{3} refers to the column precedent and antecedent and 0.5 on the sloped line -- -- a second negative/descent/derivative is provided with the help of intermediate entries-- these intermediate entries are not shown with a column heading of - since the continuous down slope shows that anyway

The manual is at -- http://ftp.cc.uoc.gr/mirrors/CTAN/macros/latex/contrib/tkz/tkz-tab/doc/tkz-tab-screen.pdf

\documentclass[12pt]{extreport}
\usepackage[left = 1in, right = 1in, top = 0.7in, bottom 
= 0.7in]{geometry}
\usepackage{graphicx,latexsym,mathtools}
\usepackage{tikz,tkz-tab}

\begin{document}

\begin{tikzpicture}

\newcommand*{\va}{\colorbox{red!50} {$\scriptscriptstyle 
V_a$}}
\newcommand*{\vb}{\colorbox{blue!50} {$\scriptscriptstyle 
V_b$}}
\newcommand*{\vbo}{\colorbox{blue!50} 
{$\scriptscriptstyle 
V_{b1}$}}
\newcommand*{\vbt}{\colorbox{yellow!50} 
{$\scriptscriptstyle 
V_{b2}$}}
\newcommand*{\vc}{\colorbox{gray!50} {$\scriptscriptstyle 
V_c$}}
\newcommand*{\vd}{\colorbox{magenta!50} 
{$\scriptscriptstyle 
V_d$}}
\newcommand*{\ve}{\colorbox{orange!50} 
{$\scriptscriptstyle 
V_e$}}
\tkzTabInit[color,
colorT = yellow!20,
colorC = red!20,
colorL = green!20,
colorV = lightgray!20,
lgt = 3,
espcl = 4]%
{$x$/1, $f_\alpha'(x)$/1, $f_\alpha(x)$/3}%
{$0$, $\alpha-1$,$+\infty$} 
\tkzTabLine{ ,+,0,-,-,, }
\tkzTabVar{-/ $0$, +/ $f_\alpha(\alpha-1)$,-/ $-\infty$}%
\tkzTabVal{2}{3}{0.5}{$x^*(\alpha)$}{0}
\end{tikzpicture}
\end{document}