Hello people! Well, I am doing some excercises for fun. Picked some Precalculus stuff, and found this excercise: "Construct a function that has the same slope at x = 1 and x = 2. Then find two points where y = x^4 - 2x^2 has the same tangent line (draw the graph)." I have found a solution, but I think the solution is totally wrong. Any advice? What I did: For the first part made up y = x^3 + 1 Then, I plotted two points: (1,2) (2,9) where (a,f(a)) and (b,f(b)). Calculated the slope and got 7. two-point form: y - 2=7(x - 1) y = 7x - 9 slope-form. Secant line. y= 7 Tangent line. For the second par did something similar: I plotted points: (2,24) (3,81) for y = x^4 - 2x^2 The slope is 57. Thw two-point form: y -24 =57(x - 2) y = 57x - 90 slope-form. Secant line. y = 57 Tangent line. It must be wrong, but I can not say why. Also tried the following: Since two points have the same tangent line, or derivative, f'(a) = f'(b) And y = x^4 - 2x^2 when x = a y = a^4 -2a^2 and y = b^2 - 2b^2 Then: f'(a) = f(a) - f(b)/ a - b f'(b) = f(b) - f(a)/ b - a End up needing to solve for two equations, but everything gets to messy, and surely must be wrong. I think I am confused. Any correction? Thanks in advanced!