findDup <- function(x) { duplicated(x) | duplicated(x, fromLast = TRUE) }

library(dplyr,warn.conflicts = FALSE) library(ggplot2,warn.conflicts = FALSE) library(forcats,warn.conflicts = FALSE) library(tidyr,warn.conflicts = FALSE) library(plotly,warn.conflicts = FALSE) library(zoo,warn.conflicts = FALSE) library(lubridate,warn.conflicts = FALSE) require(stringr) library(bigrquery,warn.conflicts = FALSE) library(shiny,warn.conflicts = FALSE) library(shinydashboard,warn.conflicts = FALSE) library(googledrive,warn.conflicts = FALSE) library(googleVis,warn.conflicts = FALSE)

setwd("C:/Users/eric.reschke/Desktop/School/DS_Math/R")

CurrentMonth <- as.Date(as.yearmon(Sys.Date()))

a <- 1 b <- -4 c <- -5

x_Addsqrt <- -b+sqrt((b^2) - (4ac)) x_Addsqrt <- x_Addsqrt/(2*a)

x_Subtractsqrt <- -b-sqrt((b^2) - (4ac)) x_Subtractsqrt <- x_Subtractsqrt/(2*a)

x_MIN <- -7 x_MAX <- 7

x_vals <- matrix(c(x_MIN:x_MAX)) slopeTableMain <- x_vals colnames(slopeTableMain) <- "x" slopeTableMain <- as.data.frame(slopeTableMain) slopeTableMain <- slopeTableMain %>% mutate(x = as.numeric(x))

slopeTable1 <- slopeTableMain %>% mutate(y = abs(x))

fx1 <- ggplot(data=slopeTable1, aes(x=x, y=y)) + geom_line()+ geom_point()+ geom_text(aes(label=y,vjust=1.5)) + scale_x_continuous(breaks = seq(x_MIN,x_MAX,1)) + ylab("f(x) = abs(x)") + ggtitle("slopeTable1")

ggplotly(fx1) fx1

slopeTable2 <- slopeTableMain %>% mutate(y = ((x+1)(x-3))/((x-6)(x+2)))

fx2 <- ggplot(data=slopeTable2, aes(x=x, y=y)) + geom_line()+ geom_point()+ scale_x_continuous(breaks = seq(x_MIN,x_MAX,1)) + ylab("f(x) = (x+1)(x-3)/(x-6)(x+2)") + ggtitle("slopeTable2")

ggplotly(fx2) fx2

slopeTable3 <- slopeTableMain %>% mutate(y = ((2*(x^2)))) %>% mutate(m = if_else(is.na(lead(y)),0, (lead(y)-y)/(lead(x)-x),0))

fx3 <-ggplot(data=slopeTable3, aes(x=x, y=y)) + geom_line()+ geom_point()+ geom_text(aes(label=y,vjust=1.5))+ scale_x_continuous(breaks = seq(x_MIN,x_MAX,1)) + ylab("f(x) = 2x+8 when x<=-2; x^2 when x>-2") + ggtitle("slopeTable3")

fx3 ggplotly(fx3)

questionFiveTable <- slopeTableMain %>% mutate(y = ((x^2) - (x+30)))

fx4 <-ggplot(data=questionFiveTable, aes(x=x, y=y)) + geom_line()+ geom_point()+ geom_text(aes(label=y,vjust=1.5)) + scale_x_continuous(breaks = seq(x_MIN,x_MAX,1)) + ylab("Revenue") + xlab("Number of Widgets (in thousands)") + ggtitle("Question #5")

ggplotly(fx4) fx4

questionFiveTable <- questionFiveTable %>% mutate(m = if_else(is.na(lead(y)),0, (lead(y)-y)/(lead(x)-x),0)) #%>% #mutate(sameSlope = m/x)

questionNineTable <- slopeTableMain %>% mutate(y = ((x^2) - (x+30)))

fx5 <-ggplot(data=questionFiveTable, aes(x=x, y=y)) + geom_line()+ geom_point()+ geom_text(aes(label=y,vjust=1.5)) + scale_x_continuous(breaks = seq(x_MIN,x_MAX,1)) + ylab("Revenue") + xlab("Number of Widgets (in thousands)") + ggtitle("Question #9")

ggplotly(fx5) fx5

questionFiveTable <- questionFiveTable %>% mutate(m = if_else(is.na(lead(y)),0, (lead(y)-y)/(lead(x)-x),0)) #%>% #mutate(sameSlope = m/x)

x = -1;

(0.25*(x^4)) - (5/3*(x^3)) + (x^2) + (8*x) - 4

(4*.25)(x^3) - (3(5/3))(x^2) + (2x) + 8

x_MIN <- -4 x_MAX <- 7

x_vals <- matrix(c(x_MIN:x_MAX)); derivativeTableMain <- x_vals; colnames(derivativeTableMain) <- "x"; derivativeTableMain <- as.data.frame(derivativeTableMain); derivativeTableMain <- derivativeTableMain %>% mutate(x = as.numeric(x))

Derivative_Function_Tbl <- derivativeTableMain %>% mutate(y = if_else(x<=4,round((x^3)+((x^2)-(16x)),2),round((x^2)-(10x),2))) %>% mutate(derivative = if_else(x<=4,round(3*(x^2)+(2x)-16),round((2x)-10,2)))

Derivative_Function_Tbl_Zero <- Derivative_Function_Tbl %>% subset(derivative==0)

derGraph <-ggplot(data=Derivative_Function_Tbl, aes(x=x, y=derivative)) + geom_line()+ geom_point()+ geom_text(aes(label=derivative,vjust=1.5))+ scale_x_continuous(breaks = seq(x_MIN,x_MAX,1)) + ylab("f(x)") + ggtitle("Derivative Tbl Graph")

derGraph ggplotly(derGraph)