# Second Derivatives and Beyond

# Critical Points Exercises

### Example 1

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

### Example 2

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

*f* (*x*) = cos *x*

### Example 3

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

### Example 4

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

### Example 5

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

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

### Example 6

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

*f* (*x*) = 4*x*^{3} + 3*x*^{2} – 2*x* + 1

### Example 7

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

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

### Example 8

or the function, find all critical points or determine that no such points exist.

*f* (*x*) = sin^{2} *x*

### Example 9

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

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

### Example 10

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

*f* (*x*) = 3*x* – 2^{x}