Answer:
[tex]2x - 6[/tex]
[tex]x=3 \rightarrow \ minimum \ point[/tex]
Step-by-step explanation:
[tex]f(x) = x^2 - 6x +36[/tex]
The derivative is: [tex]f'(x)= 2x - 6[/tex]
To calculate the max/min point of the function, we use the first derivative and put it equal to zero (if needed)
[tex]f'(x) = 2x - 6 = 0\\2x - 6 = 0\\2x = 6\\x = 3[/tex]
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.
[tex]f''(x) = 2[/tex]
The second derivative is positive, hence [tex]x = 3[/tex] is minimum.
