if( !require('NLRoot') ){
    install.packages('NLRoot')
}
library(NLRoot)

# Plot the region where the argument of the square root is positive:
# 
x = seq( -3, 3, length.out=500 )
y = function(x){ 65 - 8*exp(-x) - 8*exp(x) }
ys = y(x) 
plot( x, ys, type='l' )
abline(h=0, col='blue')
grid()

BFfzero( y, -2.5, -2 )
BFfzero( y, 2.0, 2.5 )

#postscript("../../WriteUp/Graphics/Chapter2/chap_2_sect_2_prob_18_plot.eps", onefile=FALSE, horizontal=FALSE)

x = seq( -2.0, 2.0, length.out=100 )
y = function(x){ ( -3 + sqrt( 65 - 8*exp(-x) - 8*exp(x) ) )/2 }
ys = y(x) 
plot( x, ys, type='l', xlab='x', ylab='y(x)' )
grid()

#dev.off()