Project 1. A particle moves along a straight line. The graph of the particle's position x(t) at time t is shown below over the interval [0, 10]. The function has horizontal tangents at t = 1.7 and t = 6.9, and a point of inflection at t = 4.3. Determine the values oft where the velocity of the particle is increasing. Justify your answers. x(t) 6 4+ NO -2 0 2 4 6 8 H 10 t2. Let f(x) = sin(3x) + ems *. 3) Find the slope of the line tangent to the graph of x) at x = n. b) Let h(x) be the piecewise-dened function shown in the graph. If m(x) = h(f(x)), determine m'ljr). 5 y 4+ 2- h(x) 1 -3 -2 -1 0 Not 33. Consider the curve defined as 3xzy2 = 4x2 4xy. a) Write an equation for the line tangent to the curve at the point (4,1). b) Determine the coordinates, (any), where the tangent line is vertical. 4. The function for} = r2it has a derivative where f(x) = f'(x). Determine a function where f'(x) = 2f{x)