aa=705

c=0.05
f=function(b){
   aa*(c/(b-1))^(1/b)
}
optimize(f,c(1,8))
plot(f,0.5,8,type="l",lty=1,xlab="Beta",ylab="T*")

c=0.1
f=function(b){
   aa*(c/(b-1))^(1/b)
}
optimize(f,c(1,8))
plot(f,0.5,8,add=TRUE,type="l",lty=2,xlab="",ylab="")

c=0.15
f=function(b){
   aa*(c/(b-1))^(1/b)
}
optimize(f,c(1,8))
plot(f,0.5,8,add=TRUE,type="l",lty=3,xlab="",ylab="")

c=0.2
f=function(b){
   aa*(c/(b-1))^(1/b)
}
optimize(f,c(1,8))
plot(f,0.5,8,add=TRUE,type="l",lty=4,xlab="",ylab="")

c=0.25
f=function(b){
   aa*(c/(b-1))^(1/b)
}
optimize(f,c(1,8))
plot(f,0.5,8,add=TRUE,type="l",lty=5,xlab="",ylab="")

c=0.3
f=function(b){
   aa*(c/(b-1))^(1/b)
}
optimize(f,c(1,8))
plot(f,0.5,8,add=TRUE,type="l",lty=6,xlab="",ylab="")
legend("topright",c(expression("c=0.05"),expression("c=0.1"),expression("c=0.15"),expression("c=0.2"),expression("c=0.25"),expression("c=0.3")),lty=c(1,2,3,4,5,6))<pre>An Error occurred while handling another error:
yii\web\HeadersAlreadySentException: Headers already sent in  on line 0. in /var/www/html/prof-homepages/vendor/yiisoft/yii2/web/Response.php:366
Stack trace:
#0 /var/www/html/prof-homepages/vendor/yiisoft/yii2/web/Response.php(339): yii\web\Response-&gt;sendHeaders()
#1 /var/www/html/prof-homepages/vendor/yiisoft/yii2/web/ErrorHandler.php(136): yii\web\Response-&gt;send()
#2 /var/www/html/prof-homepages/vendor/yiisoft/yii2/base/ErrorHandler.php(135): yii\web\ErrorHandler-&gt;renderException()
#3 [internal function]: yii\base\ErrorHandler-&gt;handleException()
#4 {main}
Previous exception:
yii\web\HeadersAlreadySentException: Headers already sent in  on line 0. in /var/www/html/prof-homepages/vendor/yiisoft/yii2/web/Response.php:366
Stack trace:
#0 /var/www/html/prof-homepages/vendor/yiisoft/yii2/web/Response.php(339): yii\web\Response-&gt;sendHeaders()
#1 /var/www/html/prof-homepages/vendor/yiisoft/yii2/base/Application.php(656): yii\web\Response-&gt;send()
#2 /var/www/html/prof-homepages/vendor/faravaghi/yii2-filemanager/models/Files.php(696): yii\base\Application-&gt;end()
#3 /var/www/html/prof-homepages/vendor/faravaghi/yii2-filemanager/controllers/FilesController.php(484): faravaghi\filemanager\models\Files-&gt;getFile()
#4 [internal function]: faravaghi\filemanager\controllers\FilesController-&gt;actionGetFile()
#5 /var/www/html/prof-homepages/vendor/yiisoft/yii2/base/InlineAction.php(57): call_user_func_array()
#6 /var/www/html/prof-homepages/vendor/yiisoft/yii2/base/Controller.php(180): yii\base\InlineAction-&gt;runWithParams()
#7 /var/www/html/prof-homepages/vendor/yiisoft/yii2/base/Module.php(528): yii\base\Controller-&gt;runAction()
#8 /var/www/html/prof-homepages/vendor/yiisoft/yii2/web/Application.php(103): yii\base\Module-&gt;runAction()
#9 /var/www/html/prof-homepages/vendor/yiisoft/yii2/base/Application.php(386): yii\web\Application-&gt;handleRequest()
#10 /var/www/html/prof-homepages/frontend/web/index.php(18): yii\base\Application-&gt;run()
#11 {main}</pre>