Archived
126 lines
3.9 KiB
C++
126 lines
3.9 KiB
C++
#include <graphics.h>
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#include <conio.h>
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#include <stdio.h>
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#include <math.h>
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#include <winbgim.h> // Äëÿ ðàáîòû ñ ãðàôèêîé íà Windows
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// Ôóíêöèÿ äëÿ ðàñ÷åòà çíà÷åíèÿ y = (x + 4)^2(x + 3) - 6
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double func(double x) {
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return pow((x + 4), 2) * (x + 3) - 6;
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}
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int main() {
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// Èíèöèàëèçàöèÿ ãðàôè÷åñêîãî ðåæèìà
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int gd = DETECT, gm;
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initgraph(&gd, &gm, "");
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// Óñëîâèå çàäà÷è
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setcolor(WHITE);
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outtextxy(10, 10, "Íàéäèòå íàèáîëüøåå çíà÷åíèå ôóíêöèè y = (x+4)^2(x+3) - 6");
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outtextxy(10, 30, "íà îòðåçêå [-5, -3.5].");
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// Íàéäåì çíà÷åíèÿ ôóíêöèè â ãðàíè÷íûõ òî÷êàõ è êðèòè÷åñêèõ òî÷êàõ
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double x1 = -5, x2 = -3.5;
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double x_critical1 = -4, x_critical2 = -10.0 / 3.0;
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double y1 = func(x1);
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double y2 = func(x2);
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double y_critical1 = func(x_critical1);
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double y_critical2 = func(x_critical2);
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// Íàéäåì íàèáîëüøåå çíà÷åíèå
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double max_value = y1;
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double max_x = x1;
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if (y2 > max_value) {
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max_value = y2;
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max_x = x2;
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}
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if (y_critical1 > max_value) {
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max_value = y_critical1;
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max_x = x_critical1;
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}
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if (y_critical2 > max_value) {
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max_value = y_critical2;
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max_x = x_critical2;
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}
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// Âûâîä ðåøåíèÿ íà ýêðàí
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char solutionText[500];
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sprintf(solutionText, "Íàèáîëüøåå çíà÷åíèå ôóíêöèè = %.2f ïðè x = %.2f", max_value, max_x);
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outtextxy(10, 50, solutionText);
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// Ïîñòðîåíèå ãðàôèêà ôóíêöèè íà èíòåðâàëå [-5, -3.5]
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setcolor(YELLOW);
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// Íàéäåì ðàçìåðû ãðàôè÷åñêîãî îêíà
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int width = getmaxx();
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int height = getmaxy();
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int graph_x_start = 50; // Ëåâûé êðàé ãðàôèêà
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int graph_y_start = height / 2; // Ñðåäíÿÿ ëèíèÿ äëÿ îñè y
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int graph_width = width - 100; // Øèðèíà ãðàôèêà
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// Óñòàíîâèì ìàñøòàá ïî îñè X è Y
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double x_scale = graph_width / (x2 - x1); // Ìàñøòàá ïî X
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double y_scale = 30; // Ìàñøòàá ïî Y (çàâèñèò îò ôóíêöèè)
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// Îòîáðàæàåì îñè
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setcolor(WHITE);
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line(graph_x_start, 0, graph_x_start, height); // Îñü Y
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line(0, graph_y_start, width, graph_y_start); // Îñü X
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// Ðàçìåòêà (ñåòêà)
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setcolor(LIGHTGRAY);
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// Ãîðèçîíòàëüíûå ëèíèè (ïî Y)
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for (int i = -5; i <= 5; i++) {
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int y_line_pos = graph_y_start - i * y_scale;
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line(0, y_line_pos, width, y_line_pos);
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char label[10];
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sprintf(label, "%d", i);
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outtextxy(graph_x_start - 30, y_line_pos - 5, label);
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}
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// Âåðòèêàëüíûå ëèíèè (ïî X)
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for (double i = x1; i <= x2; i += 0.5) {
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int x_line_pos = graph_x_start + (int)((i - x1) * x_scale);
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line(x_line_pos, 0, x_line_pos, height);
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char label[10];
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sprintf(label, "%.1f", i);
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outtextxy(x_line_pos - 10, graph_y_start + 10, label);
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}
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// Îòðèñîâêà ôóíêöèè
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setcolor(YELLOW);
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for (int i = graph_x_start; i < graph_x_start + graph_width; i++) {
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double x = x1 + (i - graph_x_start) / x_scale;
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double y = func(x);
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int graph_y = graph_y_start - (int)(y * y_scale);
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putpixel(i, graph_y, YELLOW);
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}
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// Îòìå÷àåì òî÷êó ìàêñèìóìà
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int max_graph_x = graph_x_start + (int)((max_x - x1) * x_scale);
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int max_graph_y = graph_y_start - (int)(max_value * y_scale);
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setcolor(RED);
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circle(max_graph_x, max_graph_y, 5);
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outtextxy(max_graph_x + 10, max_graph_y - 10, "Max");
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// Çàïèñü ðåøåíèÿ â ôàéë
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FILE *file = fopen("Ðåøåíèå_çàäà÷è.txt", "w");
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if (file == NULL) {
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printf("Îøèáêà ïðè îòêðûòèè ôàéëà!\n");
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return 1;
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}
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fprintf(file, "Íàèáîëüøåå çíà÷åíèå ôóíêöèè íà îòðåçêå [-5, -3.5]:\n");
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fprintf(file, "Ìàêñèìóì = %.2f ïðè x = %.2f\n", max_value, max_x);
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fclose(file);
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printf("Îòâåò çàïèñàí â ôàéë 'Ðåøåíèå_çàäà÷è.txt'.\n");
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// Îæèäàíèå ââîäà äëÿ çàêðûòèÿ ãðàôè÷åñêîãî îêíà
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getch();
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closegraph();
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return 0;
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}
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