Find the equation of the tangent at x3 to the curve y2x squared - 3x 2?

The tangent to the curve y = 2x2 - 3x + 2 at x=3 first we differentiate the eqution and get

dy/dx = 4x -3 feed in the x=3 dy/dx = 9 So we now know that the gradient of the tangent is 9 We can also find out one of the points that is passes through. y = 2x2 - 3x + 2 when x = 3 y = 2*32 - 3*3 + 2 y = 29 So we have a line of gradient 9 that passes through the pint (3,29) We can now find out the y intercept

29 - (3*9) = 2 y = 3x + 2