Verified answer

1) y = x⁴ + 5x³ - 2x² - 12

V = y' = (x⁴ + 5x³ - 2x² - 12)' = (x⁴)' + 5(x³)' - 2(x²)' - 12' = 4x³ + 15x² - 4x

V(5) = 4 * 5³ + 15 * 5² - 4 * 5 = 500 + 375 - 20 = 855

2) y = ax³ - bx² - c

a = 10 000 ,    b = 100,     c = 5

y = 10000x³ - 100x² - 5

V= y' = (10000x³ - 100x² - 5)' = 10000(x³)' - 100(x²)' - 5' = 30000x² - 200x

V(0,12) = 30000 * (0,12)² - 200 * 0,12 = 30000 * 0,0144 - 200 * 0,12 = =432 - 24 = 408