35. A particle travels along a curve y = f(x) as in Figure 15. Let L(t) be the particle's distance from the origin. x+ f(x)f'(x)\ dx (a) Show that dL - if the particle's location at time t is P = (x, f(x)). dt Vx² + f(x)² ) dt (b) Calculate L'(t) when x = 1 and x = 2 if f(x) = 3x² – 8x +9 and dx/dt = 4. y = f(x) FIGURE 15

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