CALCULUS
Derivatives. Velocity and Acceleration (I)
1. Find the velocity, acceleration, and jerk functions for the following position function: s(t) = t + 4t2 5t3 2. Find the velocity, acceleration, and jerk functions for the following position function:
CALCULUS
Derivatives. Tangent Line
1. Find the equation of the tangent line to the graph of the given function at the given point: f (x) = x 3x2 ; P (2, 14)
2. Find the equation of the tangent line to the graph of the given function at the given point: f
CALCULUS
Derivatives. Higher Derivatives (II) 1 2 + 2 1 x3 x 5 5 2 + 2 + + 1 4x x3 x x 2 + 4 + 5x2 + 5x3 + 2x4 x
1. Find f (x), f (x), f (x), and f (4) for the following function: f (x) =
2. Find f (x), f (x), f (x), and f (4) for the following function:
CALCULUS
Derivatives. Higher Derivatives
1. Find f (x), f (x), f (x), and f (4) for the following function: f (x) = 4 3x + 2x2 3x3 + x4 2. Find f (x), f (x), f (x), and f (4) for the following function: f (x) = 4 + 2x 2x3 + 3x4 + 5x5 3. Find f (x), f (x),
CALCULUS
Derivatives. Power and Sum/Dierence Rules
3 1 1. Dierentiate the following function:f (x) = + 4 2x2 3 x x 4 3 2. Dierentiate the following function:f (x) = 3 x13 + 3x3 + x 4 3 3. Dierentiate the following function:f (x) = 3 x10 5x10 + 6 x 4. Dier
CALCULUS
Derivatives. Tangent Line (II)
1. Find the equation of the tangent line of the slope m = 0 to the graph of the function: f (x) = 3 4x 2x2 2. Find the equation of the tangent line of the slope m = 5 to the graph of the function: f (x) = 5+5x +2x2
Answers: 5 1. f (x) = 4 x The function f is dierentiable over [0, ). 4 1 1 2. f (x) = The function f is dierentiable over R\cfw_0. 3 3 x4 4 1 3. f (x) = The function f is dierentiable over R\cfw_0. 5 5 x9 4 1 4. f (x) = The function f is dierentiable over
CALCULUS 3x 3x2 2 + x x2 1 2x2 2 2x x2 if x < 1 if x 1
Dierentiability (I)
1. Consider the following piece-wise dened function: f (x) = Analyze the dierentiability of the function f (x) at x = 1. 2. Consider the following piece-wise dened function: f (x)
CALCULUS 1. Determine the rate of change of the given function over the given interval: 2x over [4, 2] f (x) = 1 2 x + 2 x2 2. Determine the rate of change of the given function over the given interval: 2 2 f (x) = +2x + 2 + over [3, 2] +2 x x 3. Determin