- #1
Speedking96
- 104
- 0
Homework Statement
Estimate the instantaneous velocity of a particle with position function s(t) = 2t2−4t at t = 1 using the four intervals [0.9, 1], [0.99, 1], [1, 1.01], and [1, 1.1].
2. The attempt at a solution
At t=1, y = -2
Slope of a line: a = (y2 - y1)/(x2 - x1)
= (y2 + 2) / (x2 - 1)
= (2t2−4t +2) / (x2 -1)
At t = 0.9
= (2(0.9)2−4(0.9) +2) / (0.9 -1)
= -0.2
At t = 0.99
= (2(0.99)2−4(0.99) +2) / (0.99 -1)
= -0.02
At t = 1.01
= (2(1.01)2−4(1.01) +2) / (1.01 -1)
= 0.02
At t = 1.1
= (2(1.1)2−4(1.1) +2) / (1.1 -1)
= 0.2
From the graph of the parabola, it's pretty obvious that the equation of the tangent line is y= -2
But, I don't know where I'm going wrong.