max.c

#include <stdio.h>
#include <math.h>

#define MAX_X 5
#define MIN_X -6

int f(int x) {
  return (-5*pow(x, 3)) - (31 * pow(x, 2)) + (4 * x) + 31;
}

int main() {
  // assume max at the max x of given range
  int max = f(MAX_X);
  int res;

  for (int x = MIN_X; x < MAX_X + 1; x++) {
    res = f(x);

    if (res > max) {
      max = res;
    }
  }

  printf("MAX: %d", max);

  return 0;
}