Calculus 2 Parametric equations?

x = sqrt(t)

y = sqrt(t - 1)

x^2 = t

y^2 = t - 1

2x * dx = dt

dx/dt = 1/(2x)

dx/dt = 1/(2 * sqrt(t))

y^2 = t - 1

2y * dy = dt

dy/dt = 1/(2y)

dy/dt = 1/(2 * sqrt(t - 1))

(dy/dx) =>

(dy/dt) / (dx/dt) =>

(1/(2sqrt(t))) / (1/(2sqrt(t - 1))) =>

2 * sqrt(t - 1) / (2 * sqrt(t)) =>

sqrt(t - 1) / sqrt(t) =>

sqrt((t - 1) / t) =>

sqrt(1 - 1/t)

d2y/dx^2

dy/dx = sqrt((t - 1) / t)

dy/dx = sqrt(t - 1) / sqrt(t)

dy/dx = y / x

d2y/dx^2 = (x * dy/dx - x) / x^2

d2y/dx^2 = (x * (y/x) - x) / x^2

d2y/dx^2 = (y - x) / x^2

d2y/dx^2 = (sqrt(t - 1) - sqrt(t)) / t

slope

dy/dx = y/x = sqrt(t - 1) / sqrt(t)

t = 2

sqrt(2 - 1) / sqrt(2) = sqrt(1) / sqrt(2) = sqrt(2)/2

concavity

(sqrt(t - 1) - sqrt(t)) / t =>

(sqrt(1) - sqrt(2)) / 2 =>

(1 - sqrt(2)) / 2

x(t) = x? + (x? - x?) t y(t) = y? + (y? - y?) t the position (x?, y?) is initial position and (x?, y?) is position even as t = a million x(t) = 2 + (-5-2) t = 2 - 7t y(t) = 10 + (-3-10) t = 10 - 13t -------------------- speed: v(t) = ?((dx/dt)² + (dy/dt)²) v(t) = ?((-7)² + (-13)²) v(t) = ?218 v(t) ? 14.7648 instruments/sec