1. Higher Order Derivatives
Applications
and
Higher Order Derivatives
Objectives:
Be able to use the derivative to solve various applications.
Be able to find (and apply) a higher order derivative.
Critical Vocabulary:
Higher Order Derivative
Daily Warm-Up: Find the derivative using the definition of a
derivative

2. I. Applications
Example 1: (Page 283 #50) The radius of a right circular cylinder is given by and its height is where t is the time in seconds and the dimensions are in inches. Find the rate of change of the volume with respect to time.
(You will find a formula sheet on the inside cover of you textbook)

3. II. Higher Order Derivatives
s(t) = Position Function
s’(t) = v(t) = Velocity Function
s’’(t) = v’(t) = a(t) = Acceleration Function
If you differentiate the position function twice, or the velocity function once, you will yield the acceleration function
Notations:
Second Derivative: f’’(x)
Third Derivative: f’’’(x)
Forth Derivative: f(4)(x)
nth Derivative: f(n)(x)
(There are more notations in your text on page 281)

4. II. Higher Order Derivatives
Example 2: Find the second derivative: f(x) = 3x4 + 6x - 9
f’(x) = 12x3 + 6
f’(x) = 36x2
Example 3: Find f’’’(x) if f’(x) = 2x3
f’’(x) = 6x2
f’’(x) = 12x

5. II. Higher Order Derivatives
Example 4: Find f’’(x) if

6. Page 283-284 #49, 53-63 odds, 67-75 odds, 81-85 odds