Question

Find the local maxima, the local minima, the absolute maximum, and the absolute minimum of the function f(x)=x^3+x^2-2x on the interval [-2,2]. Use this inforation to sketch the graph of f.

Answer 1

find the first derivative and then set it equal to zero
f'(x)=0 for the possible critical points

Answer 2

and then?

Answer 3

u got the values of x?

Answer 4

yep

Answer 5

f'(x)=3x^2+2x-2=0
solve it fo rx

Answer 6

for x*

Answer 7

x=(-1+/- sqrt(4))/3

Answer 8

i got suqare root of 7 instead of 4.

Answer 9

oh, yes 7 is right

Answer 10

next find f''(x) and check the singn at these values of x

Answer 11

f''(x)=6x+2

Answer 12

ok

Answer 13

if f''(x) is positive, x is the point of relative minimum, if negative it is relative maximum

Answer 14

relative mean local

Answer 15

ok

Answer 16

how to draw the graph?

Answer 17

did u find the absolute max n min?

Answer 18

absolute max n min? i found relative maximum and minimum

Answer 19

for graph, u have to check the behaviou of the function in the neighbourhood of these points, mean whether the function ai increasing or decreaing

Answer 20

Can you teah me about drawing?

Answer 21

u can find absolute max and min at the extreme points of the interval

Answer 22

check the graph

Answer 23

thanks.

Answer 24

http://www.wolframalpha.com/input/?i=x^3%2Bx^2-2x%2Cfrom+x%3D-2+to+x%3D2