Question

A) What is the derivative of x^2 - 6x +36.

b) Does this function have any maximum or minimum point?

Answer 1

2x-6

Explanation:

Answer 2

`2x - 6`

`x=3 \rightarrow \ minimum \ point`

Explanation:

`f(x) = x^2 - 6x +36`

The derivative is:
`f'(x)= 2x - 6`

To calculate the max/min point of the function, we use the first derivative and put it equal to zero (if needed)

`f'(x) = 2x - 6 = 0\\2x - 6 = 0\\2x = 6\\x = 3`

To check whether this point is max or min, we substitute the value of x in the second derivative of the function. If the answer is positive, the value is minimum. If the answer is negative, the value is minimum.

`f''(x) = 2`

The second derivative is positive, hence
`x = 3` is minimum.