Question

For y = -x^4+2x^2+2 on the interval [-3, 2] what would be the absolute min/max and local min/max?

Answer 1

differentiate the function . set the derivative equal to zero solve for x to get critical points .

Answer 2

Well I know the derivative would be 4x^3+4x
And the critical points are -1, 0, and 1

Answer 3

and this would be the sign graph right?

Answer 4

you sure these are the critical points ?

Answer 5

yea
-4x^3+4x
-4x(x^2-1)=0
------------------
-4x=0
x^2-1=0
------------------
x=0/-4=0
(x+1)(x-1)=0
------------------
x=0, -1, 1

Answer 6

ok , i was confused when you said above derivative is 4x^3+4x !!!

ok f'(x)=-4x^3+4x
-4x^3+4x=0
x=0,-1,1

evaulate the function f(x) at the critical points .let me know what you get

Answer 7

for example evaulating the function at critical point 0
put x=0 in the given function
y=f(0)=(0)^4+2(0)^2+2=2
similarly find f(1) and f(-1).

Answer 8

I don't really have trouble with that kind of stuff, I just need help on telling the difference between a local ma/min and an absolute max/min

Answer 9

Like, how can you tell if a point is an abs max and a relative max or just an abs max? How can some points be both?

Answer 10

ok the largest max value a function will have is its absolute maxima
the lowest minmium value a function willl have its abosolute minima

in the given function evaluate the function at x=0 ,1,-1 also at the end points x=-3 and x=2

so
f(0)=2
f(1)=5
f(-1)=5
f(-3)=105
f(2)=26


the largest value is at x=-3 105 which is absolute maxima of the function

the smallest value is at x=0 which is the absolute minima of the function .

Answer 11

Oh, well I could agree with on the max but I had the same thing you have for min, but I got it marked wrong

Answer 12

i don't know why your teacher marked it as wrong because its the smallest pssible value in the interval [-3,2] the function will take . that is 2.

Answer 13

I don't know either.. but she hasn't been wrong yet

Answer 14

@satellite73

Answer 15

Would you use the second derivative test for anything on this?

Answer 16

check them

Answer 17

you are looking for the absolute max and min
check the critical points, i.e. plug them in
check the endpoints of the interval
the biggest is the max and the smallest is the min

Answer 18

however i think \(f(1)=3\)

Answer 19

also \(f(-1)=3\)

Answer 20

it is \( f(x) = -x^4+2x^2+2\) right?

Answer 21

mistake i think was using \(x^4+2x^2+2\) and dropping the minus sign

Answer 22

yup i missed minus sign.