Calculus, 2ADV C4 2011 HSC 4c The gradient of a curve is given by `dy/dx = 6x-2`. The curve passes through the point `(-1, 4)`. What is the equation of the curve? (2 marks) --- 5 WORK AREA LINES (style=lined) --- Show Answers Only `y = 3x^2-2x-1` Show Worked Solution `dy/dx = 6x-2` `y` `= int 6x-2\ dx` `= 3x^2-2x + c` `text{Since it passes through}\ (-1,4),` `4` `= 3 (-1)^2-2(-1) + c` `4` `= 3 + 2 + c` `c` `= -1` `:. y = 3x^2-2x-1`