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.

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