Question 1

A model for revenue is \(R(t) = 5t^4 - 3t^2 + 7\). What is \(R'(t)\)?

# install.packages("Deriv")
library(Deriv)
R <- function(t) {
  5 * t^4 - 3 * t^2 + 7
}
R_prime <- Deriv(R)
R_prime
## function (t) 
## {
##     .e1 <- t^2
##     t * (10 * .e1 + 2 * (5 * .e1 - 3))
## }

Question 2

What is the greatest common factor of 75 and 135?

# install.packages("pracma")
library(pracma)
gcd(a = 75,b = 135)
## [1] 15

Question 3

Calculate descriptive statistics for the data below.

# install.packages("summarytools")
library(summarytools)
numbers <- c(25,19,21,4,16,56,20,6,37,25,17,38,19,29,10,105,26,12,7,39)
descr(numbers)
## Descriptive Statistics  
## numbers  
## N: 20  
## 
##                     numbers
## ----------------- ---------
##              Mean     26.55
##           Std.Dev     22.50
##               Min      4.00
##                Q1     14.00
##            Median     20.50
##                Q3     33.00
##               Max    105.00
##               MAD     12.60
##               IQR     16.00
##                CV      0.85
##          Skewness      2.08
##       SE.Skewness      0.51
##          Kurtosis      4.69
##           N.Valid     20.00
##                 N     20.00
##         Pct.Valid    100.00