How do you find all critical point and determine the min, max and inflection given f(x)=3x^2-4x+1?

1 Answer
Dec 18, 2016

Critical point x=2/3
Minima -1/3
No maxima, no inflection point.

Explanation:

Find f'(x) = 6x-4. Equate it to 0 to get x=2/3. This is the only critical point.

Now find f"(x) =6, which is a positive number (irrespective of any x) . Hence, there is a minima at x=2/3. The minima would be 3(2/3)^2 -4(2/3) +1

= -1/3

Maxima does not exist.

Since f"(x) != 0, there is no inflection point.