Question

f(x)=3x^2-12x+5, find the absolute max and min value of f(x) on the interval [0,1]. From f'(x), i found x=2. Is this valid to use it on f(x) to check the min/max value? Or is it out of the interval?

Answer 1

yes, you can use it on f(x) to get the max/min value

Answer 2

but the function wil only have a minimum value, the max value is infinity

Answer 3

this interval [0,1]. is this means x,y format? or x=0 and x=1

Answer 4

oh, i didnt see there's an interval.
you can't use x=2 then

Answer 5

so i found that f(0) is the maximum, and f(1) is the minimum. Is this correct?

Answer 6

i think so
f(0) = 5 and f(1) = abs(-4) = 4

Answer 7

and also out of question, the f''(x) can be used for finding local max min, yes?

Answer 8

i have f''(x) =6, and i need to find local min max in interval [1,infinity]

Answer 9

yes, from wikipedia : If then has a local maximum at .
If then has a local minimum at .
If , the second derivative test says nothing about the point , a possible inflection point.

Answer 10

if f''(x) < 0 then f(x) has a local maximum at x
if f''(x) > 0 then f(x) has a local minimum at x

Answer 11

then for my problem is i dont have local maximum? since i have only f''(x)= 6 which is > 0

Answer 12

yes you dont, the function only has one minimum point

Answer 13

thank you, that was very helpful. :)

Answer 14

you're welcome