Find the values of x that minimize and maximize f(x)?

Question

Using calculus (first, second deriv., etc)

2. Suppose f (x) = (x^3) − (6x^2) +9x deﬁned on [0, 2]. Find the values of x that maximize 
and minimize f (x). Also ﬁnd the maximum and minimum values of f (x). 
3. Suppose f (x) = (x^3) − (6x^2) deﬁned on [2, 5]. Find the values of x that maximize and 
minimize f (x). Also ﬁnd the maximum and minimum values of f (x). 

What exactly does the question want me to do when it says "maximize and minimize?" What's the difference between finding the min and max values?

? · Accepted Answer

Solve the first derivative and find x if f'(x)=0
then solve second derivative. Instead x of f'(x) in f"(x)

if f"(x)>0 it is min
if f"(x)<0 it is max
if f"(x)=0 it is not min or max

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Find the values of x that minimize and maximize f(x)?

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