Question

Finding local and absolulute maxima and minima?
For instance in roder to solve y=3x^4 + 4x^3-12x^2+5 I know that I need to find the derivative first
f ' (x)= 12x^3+12x^2-24x
Then I factored it and got x=0 ,x=1 and x=-2 as critical points. Then I graphed a "sign" table and already know that the sequnce is decreasing,increasing,decreaing and increasing. Then plugged in all values of critical points f(0)=(0,5) f(1): (0,5) and f(-2): (-2,-27) .

Now I dont know how to distinguish local and absolute maxima and minima . Please elaborate ,since I am confued from this point on.I can do everything

Answer 1

you know "increasing, decreasing" you said, around x = -2
that means x = -2 gives a local max because the function is going up and then down

Answer 2

if it is decreasing and then increasing, evidently you have a local min, because it was going down, then going up
that is how you tell

Answer 3

how should I distinguish bthe absolue max and min

Answer 4

I mean how can I find the absmax in this problem

Answer 5

well this is a 4th degree polynomial with positive leading coefficient, so there is no way it has global max as it goes to infinity

Answer 6

it will have a minimum however

Answer 7

how should I distinguish it from the other local min

Answer 8

not sure what you are asking. you have two local mins. the smallest is the global one as well

Answer 9

I see
Thanks

Answer 10

you have two local mins, one at \(x=-2\) and the other at \(x=1\) you need to check to see what is smaller, \(f(-2)\) or \(f(1)\)

Answer 11

yw