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 of t where the velocity of the particle is increasing. Justify your answers. \f2. Let f(x) = sin(3x) + ecosx and g(x) be a differentiable function with values given in the table. a) Find the slope of the line tangent to the graph of f (x) at x = T. b) Let h(x) be the piecewise define function shown in the graph. If m(x) = h(f (x)), determine m' (It)\f3. Consider the curve dened as 3x2y2 = 4x2 4xy. a) Write an equation for the line tangent to the curve at the point (4,1). b) Determine the coordinates, (x, y), where the tangent line is vertical. 4. The function f (x) = e" has a derivative where f (x) = f'(x). Determine a function where f '(x) = 2 f (x)