math help please - understanding

Question

Answer 1

4.1)

The function is

Using first principle (limit definition of a derivative)

Answer 2

4.2)

The function is

Differentiate on each side with respect to x.

Answer 3

4.3)

The function is

Differentiate on each side with respect to x.

Product rule of differentiate :

Answer 4

4.4)

Step 1:

The function is

Differentiate on each side with respect to x.

Find number of turns.

The differentiate function is has greatest power is 2.

Hence, The graph of the function is 2 turns.

Find maximum and minimum points.

Step 2:

Graph:

Graph the function

Observe the graph:

The number of turns is two.

The maximum point is 

The minimum point is 

Solution: