Find the area of the region bounded by the parabola y = 5x^2 , the tangent line to this parabola at (3, 45) and the x-axis. Area = ?

Slope of tangent= 10x so at (3,45) it would be = 30 Equation of tangent is y-3=30(x-45) y=30x-45 it cut the parabola at exactly one point. So the required area = 1/2*(45/30)*45= 45*3/4 = 135/4 =33.75