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

1 Answer
bp
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.

Related questions
See all questions in Critical Points of Inflection
Impact of this question
1473 views around the world
You can reuse this answer
Creative Commons License