The equation of a curve C is given by y=-x^2+4x+5.Find the points on the curve C at which the tangent to C passes through the point (0,6) Answer:(-1,0) and (1,8)
I did the question by differentiating the curve (-2x+4) and set it equal to the slope formula (change in y / change in x) and substituting the x in -2x+4 with 0, but with that equation I only got the quadratic equation which -2x^2+2x+1=0, which gives me the second answer. I then tried doing it without substituting the zero, which gave me both answers. Does this work? Why did my first try only give me one answer? Thanks.