The curve C has equation y=3x^3-11x+1/2. The point P has coordinates (1, 3) and lies on C . Find the equation of the tangent to C at P.

In order to find the gradient of a tangent to the curve C we must differentiate our equation for C.dy/dx= 9x²-11To find the gradient of a tangent at a specific point P we substitute the coordinates of P into this gradient equation.dy/dx= 9(1)²-11= -2, which tells us that the gradient of the tangent at P is-2.The general equation of a line is (y-y_p)=m(x-x_p).To find the equation of our tangent to C at P we must substitute the gradient and the coordinates of P into this general equation of a line.y-3= -2(x-1)y-3= -2x +2y+2x= 5, which is our equation of the tangent to C at P.