Find the coordinates of the minimum point of the function y=(x-5)(2x-2)

At the minimum point the gradient is zero so dy/dx=0. To find dy/dx, first expand out the brackets so y=2x^2 - 12x + 10. Using differentiation dy/dx=4x - 12. At the minimum 4x-12=0 so 4x=12 therefore x=3. Put this back into the original equation to find the y value of the minimum point y=(3-5)(2x3-2)=-8