# Second Derivatives and Beyond

### Example 1

For the function, find all points of inflection or determine that no such points exist.

*f* (*x*) = sin *x*

### Example 2

For the function, find all points of inflection or determine that no such points exist.

*f* (*x*) = *e*^{x}

### Example 3

For the function, find all points of inflection or determine that no such points exist.

### Example 4

For the function, find all points of inflection or determine that no such points exist.

### Example 5

For the function, find all points of inflection or determine that no such points exist.

*f* (*x*) = 5*x* + 2

### Example 6

For the function, find all points of inflection or determine that no such points exist.

*f* (*x*) = *x*^{1/3}

### Example 7

For the function, find all points of inflection or determine that no such points exist.

*f* (*x*) = *xe*^{x}

### Example 8

For the function, find all points of inflection or determine that no such points exist.

### Example 9

For the function, find all points of inflection or determine that no such points exist.

*f* (*x*) = *x ln* *x* for *x* > > 0

### Example 10

For the function, find all points of inflection or determine that no such points exist.

The logistic equation