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nalin [4]
2 years ago
13

A continuous and differentiable function f(x) with the following properties: f(x) is decreasing at x=−5 f(x) has a local minimum

at x=−2 f(x) has a local maximum at x=2
Computers and Technology
1 answer:
butalik [34]2 years ago
7 0

The continuous and differentiable function where f(x) is decreasing at x = −5 f(x) has a local minimum at x = −2 f(x) has a local maximum at x = 2 is given as: y = 9x - (1/3)x³ + 3.

<h3>What is a continuous and differentiable function?</h3>

The continuous function differs from the differentiable function in that the curve obtained is a single unbroken curve in the continuous function.

In contrast, if a function has a derivative, it is said to be differentiable.

<h3>What is the solution to the problem above?</h3>

It is important to note that a function is differentiable when x is set to a if the function is continuous when x = a.

Given the parameters, we state that

f'(5) < 0; and

x = -5

The local minimum is given as:
x = -3;

the local maximum is given as

x = 3

Thus, x = -3 ; alternatively,

x = 3.  With this scenario, we can equate both to zero.

Hence,

x + 3 = 0;

3-x = 0.

To get y' we must multiply both equations to get:

y' = (3-x)(x + 3)

y'   = 3x + 9 - x² - 3x

Collect like terms to derive:

y' = 3x - 3x + 9 - x²; thus

y' = 9-x²

When y' is integrated, the result is

y = 9x - (x³/3) + c

Recall that

F (-5) < 0

This means that:

9 x -5 - (-5³/3) + c < 0
⇒ -45 + 125/3 + c <0
⇒ -10/3 + c < 0

Collecting like terms we have:
c < 10/3; and

c < 3.33


Substituting C into

f(x) = 9x - x³/3 + c; we have

f(x) = 9x - x³/3 + 3, which is the same as  y = 9x - (1/3)x³ + 3.

Learn more about differentiable functions at:
brainly.com/question/15047295
#SPJ1

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#include <iostream>

#include <fstream>

#include <string>

#include <iomanip>

#include "Date.h"

#include "Person.h"

using namespace std;

const int MAXSIZE = 50;

// Prototypes go here

int loadArray(string fileName, Person students[]);

void sortByName(Person students[], int numE);

void printStudentReport(Person students[], int numE);

int main()

{

Person students[MAXSIZE];

int numE;

string fileName;

cout << "Enter the file name: ";

cin >> fileName;

numE = loadArray(fileName, students);

cout << endl;

cout << "Before Sort: " << endl;

printStudentReport(students, numE);

sortByName(students, numE);

cout << endl;

cout << "After Sort: " << endl;

printStudentReport(students, numE);

return 0;

}

int loadArray(string fileName, Person students[]){

ifstream in;

in.open(fileName.c_str());

if(in.fail())

return -1;

int n=0;

string fname, lname;

int month, day, year;

while(!in.eof()){

in>>fname>>lname>>month>>day>>year;

students[n] = Person(fname, lname, Date(month, day, year));

n++;

}

return n;

}

void sortByName(Person students[], int numE){

for(int i=0; i<numE; i++){

for(int j=i+1; j<numE; j++){

if(students[i].getLastName()>students[j].getLastName()){

Person temp = students[i];

students[i] = students[j];

students[j] = temp;

}

}

}

}

void printStudentReport(Person students[], int numE){

for(int i=0; i<numE; i++){

cout<<students[i].getLastName()<<", "<<students[i].getFirstName()<<"\t\t"<<students[i].getDateofBirth().toString()<<endl;

}

}

Person.h

#include<iostream>

#include<string>

using namespace std;

#include "Date.h"

#ifndef PERSON_H

#define PERSON_H

class Person{

private:

string firstName;

string lastName;

public:

Date dateOfBirth;

Person();

Person(string firstName, string lastName, Date dob);

string getFirstName();

string getLastName();

Date getDateofBirth();

void setFirstName(string fname);

void setLastName(string lname);

void setDateOfBirth(Date dob);

void setDateOfBirth(int month, int day, int year);

};

#endif

Person.cpp

#include "Person.h"

Person::Person(){

firstName = "";

lastName = "";

}

Person::Person(string firstName, string lastName, Date dob){

this->firstName = firstName;

this->lastName = lastName;

setDateOfBirth(dob.getMonth(), dob.getDay(), dob.getYear());

}

string Person::getFirstName(){

return firstName;

}

string Person::getLastName(){

return lastName;

}

Date Person::getDateofBirth(){

return dateOfBirth;

}

void Person::setFirstName(string fname){

firstName = fname;

}

void Person::setLastName(string lname){

lastName = lname;

}

void Person::setDateOfBirth(Date dob){

setDateOfBirth(dob.getMonth(), dob.getDay(), dob.getYear());

}

void Person::setDateOfBirth(int month, int day, int year){

dateOfBirth.setMonth(month);

dateOfBirth.setDay(day);

dateOfBirth.setYear(year);

}

Date.h

#include<iostream>

#include<string>

using namespace std;

#ifndef DATE_H

#define DATE_H

class Date{

private:

int day;

int month;

int year;

public:

Date();

Date(int month, int day, int year);

int getMonth();

int getDay();

int getYear();

void setMonth(int month);

void setDay(int day);

void setYear(int year);

string toString();

};

#endif

Date.cpp

#include "Date.h"

Date::Date(){

month = 1;

day = 1;

year = 1900;

}

Date::Date(int month, int day, int year){

this->month = month;

this->day = day;

this->year = year;

}

int Date::getMonth(){

return month;

}

int Date::getDay(){

return day;

}

int Date::getYear(){

return year;

}

void Date::setMonth(int month){

this->month = month;

}

void Date::setDay(int day){

this->day = day;

}

void Date::setYear(int year){

this->year = year;

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string Date::toString(){

string ans = to_string(month)+"/";

ans += to_string(day)+"/";

ans += to_string(year);

return ans;

}

Kindly check the code output below.

4 0
3 years ago
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