Review: Derivatives Part 2

•Below is the graph of f(x). Sketch the graph of the derivative.

•The graph of the derivative is given below. Sketch the graph of f(x) given that f(-5) = 9.

A particles position is defined by s(t) = 2t3 + 3t2 – 12t. For all values of t.1) Describe the motion of the particle.

2) Determine the particles acceleration each time the velocity is zero.

Below is the graph of v(t) for a certain particle. 1. Determine when the particle is moving up.2. Determine when the particle is moving down.3. Determine when the particle is standing still.

Below is the graph of v(t) for a certain particle. 1. Determine when the particles acceleration is positive.2. Determine when the particles acceleration is negative3. Determine when the particles acceleration is zero.

Below is the graph of s(t) for a certain particle. 1. Determine when the particle is moving up.2. Determine when the particle is moving down.3. Determine when the particle is standing still.

Hot water is dripping through a coffeemaker, filling a large cup with coffee. The amount of coffee in the cup at time t, is given by a differentiable function C, where t is measured in minutes. Selected values of C(t), measured in ounces, are given in the table.

• Use the data in the table to approximate Show the computations that lead to your answer, and indicate units of measure.t(minutes) 0 1 2 3 4 5 6C(t) ounces

0 5.3 8.8 11.2 12.8 13.8 14.5

(1.5).C