## Warning: package 'Deriv' was built under R version 3.3.3
## installed_and_loaded.packages.
## prettydoc TRUE
## stats TRUE
## Deriv TRUEUsing R, provide the solution for any exercise in either Chapter 4 or Chapter 7 of the calculus textbook. If you are unsure of your solution, post your concerns.
Chapter 4.3
- Find the maximum product of two numbers (not necessarily integers) that have a sum of 100.
max_value <- 1000
min_value <- -max_value
fx <- function(x) {
x * (100 - x)
}
fxprime <- Deriv(fx)
out_root <- uniroot(fxprime, c(min_value, max_value))
fx(out_root$root)## [1] 2500x <- seq(min_value, max_value)
plot(x, fx(x))
abline(out_root$root, out_root$f.root, col = "red")
- Find the minimum sum of two numbers whose product is 500.
\(\lim x \rightarrow 0^- f(x) = -\infty\)
max_value <- 100
min_value <- -max_value
fx <- function(x) {
x + 500/x
}
fxprime <- Deriv(fx)
(out_root <- uniroot(fx, c(min_value, max_value)))## Warning in uniroot(fx, c(min_value, max_value)): NA/Inf replaced by maximum
## positive value## $root
## [1] -9.536737e-05
##
## $f.root
## [1] -5242883
##
## $iter
## [1] 22
##
## $init.it
## [1] NA
##
## $estim.prec
## [1] 9.536737e-05