[2 marks] B2(a): Using the definition of derivative, find the derivative of f(x) = x? +3. [2 marks] B2(b): The position of a particle travelling along a horizontal line int seconds is s(t) = 2t - 12t? - 72t + 8 meters. Determine the acceleration of the particle when the velocity is 0. [2 marks] B2(c): Find dy for y = cot-(8 - x). da [2 marks] B3(a): Find the critical points of the function f(x) = 823 - 24c. [4 Marks] B3(b): Apply Rolle's theorem for the function f(x) = 6x2 24x + 18 over the interval [1,3]. Justify your answer. [4 Marks] B4(a): Verify Mean value theorem for the function f(x) = 8x* over the interval (0,2). [2 marks] B4(b): A ball is dropped from certain height, its position at time t is s(t) = -8+32 find the time t when ball hits the ground. [4 Marks] B5(a): For the function f(x) = 8.23 48xdetermine ) Intervals where f is increasing and decreasing, (ii) Intervals where f is concave up and concave down. [2 marks] B5(b): Evaluate: [*e +6)8 + 2)dt