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Second Derivatives and Beyond

Second Derivatives and Beyond

Example 1

Let (x) = x3 + 2.

Find 2(x).

Example 2

Let (x) = x3 + 2.

Find (2)(x).

Example 3

Suppose f (x) is a degree 3 polynomial.

a. What is the degree of '(x)?

b. What is the degree of f (2)(x) ?

c. What is the degree of f (3)(x) ?

Example 4

Suppose f (x) is a degree 9 polynomial.

a. What is the degree of f 8(x) ?

b. What is the degree of f 9(x)?

c. What is the degree of f 10(x)?

Example 5

Suppose f (x) is a degree n polynomial.

a. What is the degree of f (n - 1)(x)?

b. What is the degree of f (n)(x)?

c. What is the degree of f (k)(x) where k is any integer greater than n?

Example 6

Exercise. Find the first nine derivatives of the function f (x) = sin x.

Example 7

Let f (x) = sin x. Find the derivative.

f (12)(x)

Example 8

Let f (x) = sin x. Find the derivative.

f (22)(x)

Example 9

Let f (x) = sin x. Find the derivative.

f (33)(x)

Example 10

What are some functions that are infinitely differentiable?

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