Consider a particle moving along the x-axis where x(t) is the position of the particle at time t, x'(t) is its velocity, and x"( is its acceleration. x(t) = t3 - 12t2 + 21t - 3, osts 10 (a) Find the velocity and acceleration of the particle. x'(t) = x"(t) = (b) Find the open t-intervals on which the particle is moving to the right. (Enter your answer using interval notation.) (c) Find the velocity of the particle when the acceleration is 0.

Suppose the tangent line to the curve y = f(x) at the point (7,9) has the equation y = -3x + 30. If Newton's method is used to locate a root of the equation f(x) = 0 and the initial approximation is x1 = 7, the second approximation x2

Let f(t) = (t² + 7t + 6) (5t² + 3). Find ƒ'(t). f'(t) = Find f'(5). ƒ'(5) =