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Vedmedyk [2.9K]
2 years ago
10

Consider the graph of the function f(x) = 2(x + 3)2 + 2. Over which interval is the graph decreasing? (–∞, –3) (–∞, 2) (–3, ∞) (

2, ∞)
Computers and Technology
2 answers:
Vaselesa [24]2 years ago
6 0

Answer:

The interval over which the graph is decreasing is;

(-∞, -3)

Explanation:

The given function is f(x) = 2·(x + 3)² + 2

By expanding the function, we have;

2·x² + 12·x + 20

From the characteristics of a quadratic equation, we have;

The shape of a quadratic equation = A parabola

The coefficient of x² = +2 (positive), therefore the parabola opens up

The parabola has a minimum point

Points to the left of the minimum point are decreasing

The minimum point is obtained as the x-coordinate value when f'(x) = 0

∴ f'(x) = d(2·x² + 12·x + 20)/dx = 4·x + 12

At the minimum point,  f'(x) = 4·x + 12 = 0

∴ x = -12/4 = -3

Therefore;

The graph is decreasing over the interval from -infinity (-∞) to -3 which is (-∞, -3)

Please find attached the graph of the function created with Microsoft Excel

The graph is decreasing over the interval (-∞, -3).

Annette [7]2 years ago
4 0

Answer:

A. (–∞, –3)

Explanation:

Edge 2021 ( if feel still think it's wrong, check the picture ⬇️  )

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#include <stdio.h>

#define MAX_SIZE 50

#define password "mypassword"

void addProduct(struct product arr[], struct product p);

void deleteProduct(struct product arr[], char[] productId)

void editProduct(struct product arr[], int incrementKey, char[] productId) //incrementKey is the how much quanity user wants to add of the existing product

void display(struct product arr[]);

void saleProduct(struct product arr[], char[] productId, int soldItems);

void displayHighestSaleProduct(struct product arr[]);

void displayProductWithZeroQuantity(struct product arr[]);

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struct product

{

char id[10]; //product id

char name[50]; //name of product

int quantity; //number of items of product in the inventory

int numSold; //number of items sold

float price; //price of the product

float sales; //total sale

};

void saleProduct(struct product arr[], char[] productId, int soldItems)

{

int index = 0;

while(strcmp(arr[index].id, productId) != 0) //getting the index of product same as productId

index++;

arr[index].qunatity -= soldItems;

arr[index].sales += (soldItems*arr[index].price);

}

void displayProductWithZeroQuantity(struct product arr[])

{

int x = 0;

printf("Zero Quantity Product:");

for(int i=0;i<totalItems;i++)

if(arr[i].qunatity == 0)

{

printf("Id=>%s\tName=>%s\tQuantity=>%d\tNumSold=>%.2f\tPrice=>%d\tSales=>%.2f", &arr[i].id, &arr[i].name, &arr[i].quantity, &arr[i].numSold, &arr[i].price, &arr[i].sales);

x = 1;

}

if(x == 0)

printf("No product with zero quantity.");

}

void displayHighestSaleProduct(struct product arr[])

{

float max = 0.0f;

int index = 0;

for(int i=0;i<totalItems;i++)

if(arr[i].sales > max)

{

max = arr[i].sales;

index = i;

}

printf("Highest saling product:");

printf("Id=>%s\tName=>%s\tQuantity=>%d\tNumSold=>%.2f\tPrice=>%d\tSales=>%.2f", &arr[index].id, &arr[index].name, &arr[index].quantity, &arr[index].numSold, &arr[index].price, &arr[index].sales);

}

void display(struct product arr[])

{

for(int i=0;i<totalItems;i++)

{

printf("Id=>%s\tName=>%s\tQuantity=>%d\tNumSold=>%.2f\tPrice=>%d\tSales=>%.2f", &arr[i].id, &arr[i].name, &arr[i].quantity, &arr[i].numSold, &arr[i].price, &arr[i].sales);

printf("\n");

}

}

void editProduct(struct product arr[], int incrementKey, char productId[])

{

int index = 0;

while(strcmp(arr[index].id, productId) != 0) //getting the index of product same as productId

index++;

arr[index].quantity += incrementKey ;

}

void addProduct(struct product arr[], struct product p)

{

int index = 0;

while(index < totalItems)

index++;

arr[index] = p;

totalItems++;

}

void deleteProduct(struct product arr[], char[] productId)

{

int index = 0;

while(strcmp(arr[index].id, productId) != 0) //getting the index of product same as productId

index++;

for(int i = index;i<totalItems-1;i++)

arr[i] = arr[i+1] ;

totalItems--;

}

void processintChoice(int x, struct product arr)

{

switch(x)

{

case 1:

{

char id[10];

char name[50];

int quantity;

float price;

printf("\nenter the id of product:");

scanf("%s", &id);

printf("\nenter the name of product:");

scanf("%s", &name);

printf("\nenter the quantity of product:");

scanf("%d", &quantity);

printf("\nenter the price of product:");

scanf("%.2f", &price );

struct product p;

p.id = id;

p.name = name;

p.quantity = quantity;

p.price = price;

p.numSold = 0;

p.sales = 0.0f;

addProduct(arr, p);

}

case 2:

{

char str[10];

int num;

printf("enter the product id");

scanf("\n%s", &str);

printf("enter the number by which you want to increase product items.")

scanf("\n%d", &num);

editProduct(arr, num ,str);

}

case 3:

{

char p[10];

printf("enter the product id to delete product:");

scanf("\n%s", &p);

deleteProduct(arr, p);

}

case 4:

{

display(arr);

}

case 5:

{

char p[10];

int num;

printf("enter the product od to purchse:");

scanf("\n%s", &p);

printf("enter the number of items u want to purchse:");

scanf("\n%d", &num);

saleProduct(arr, p, num);

}

case 6:

{

displayHighestSaleProduct(arr);

}

case 7:

{

displayProductWithZeroQuantity(arr);

}

case 8:

{

exit(0);

}

}

}

int main()

{

struct product arr[MAX_SIZE];

char pass[10];

printf("please enter the password:")

scanf("\n%s", &pass);

if(strcmp(pass, password) == 0)

{

label:

printf("\nplease select the proper option from the below menu:");

printf("\n1.) Input new product record");

printf("\n2.) Edit a product");

printf("\n3.) delete a product");

printf("\n4.) display all existing products");

printf("\n5.) make a purchase");

printf("\n6.) display the product detail with highest sale");

printf("\n7.) display a product with zero quantity");

printf("\n8.) exit the program");

int choice;

printf("\nChoice - >");

scanf("%d", &choice);

if(choice < 1 && choice > 8 )

{

printf("Invalid Choice! please choose again");

goto label;

}

else

processChoice(choice, arr);

}

else return(0);

}

3 0
3 years ago
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