F.4 Maths Further practice

1)y = (2x - 1)(3 - 7x)= 6x - 3 - 14x² + 7x= - 14x² + 13x - 3= - 14[x² - (13/14)x] - 3= - 14[x² - 2(13/28)x + (13/28)² - (13/28)²] - 3= - 14(x - 13/28)² + 14(13/28)² - 3= - 14(x - 13/28)² + 1/56When x = 13/28 , the max. value of y = 1/56.
2)y = (1/3)(3x - 2)(5 - x)= (1/3)(15x - 10 - 3x² + 2x)= - (1/3)(3x² - 17x + 10)= - [x² - (17/3)x + 10/3]= - [x² - 2(17/6)x + (17/6)² + 10/3 - (17/6)²]= - [(x - 17/6)² - 169/36]= - (x - 17/6)² + 169/36When x = 17/6 , the max. value of y = 169/36