A particle is moving along a curve where x(t) = t² - 4t + 8 and y(t) is not explicitly given and dy/dt = teᵗ⁻³ - 1 a. Find the time 0 ≤ t ≤ 4, when the line tangent to the path of the particle is horizontal. b. Is the direction of the motion of the particle towards the left or right at that time? Explain.