12. What is the y coordinate of the point on the curve y = 2x² – 3x at which the slope of the tangent line is the same as that of the secant line between x = 1 and x = 2?

Since the given curve is continuous on the closed interval [1,2] and differentiable on the open interval (1,2), then by the mean value theorem there exist a number c in (1,2) such that

Which says that the slope of the tangent line at c is equivalent to the slope of the secant line between x = 1 and x = 2. Since, f’(x) = 4x – 3

Thus, the y coordinate is,