Math Questions and Answers

Start Your Free Trial

`f(x) = 3x^4 - 4x^3 - 12x^2 + 1, [-2, 3]` Find the absolute maximum and minimum values of f on the given interval

Expert Answers info

mathace eNotes educator | Certified Educator

calendarEducator since 2015

write489 answers

starTop subject is Math

Given: `f(x)=3x^4-4x^3-12x^2+1,[-2,3].`

Find the critical numbers by setting the first derivative equal to zero and solving for the x value(s).

`f'(x)=12x^3-12x^2-24x=0`

`12x(x^2-x-2)=0`

`12x(x-2)(x+1)=0`

`x=0,x=2,x=-1` 

The critical numbers are x=0,x=2, and x=-1. Plug in the critical numbers and the endpoints of the interval [-2,3] into the original f(x) function.

f(-2)=33

f(-1)=-4

f(0)=1

f(2)=-31

f(3)=28

Examine the f(x) values to determine the absolute maximum and...

(The entire section contains 2 answers and 252 words.)

Unlock This Answer Now


check Approved by eNotes Editorial

gsarora17 eNotes educator | Certified Educator

calendarEducator since 2015

write762 answers

starTop subjects are Math, Science, and Business


check Approved by eNotes Editorial