Question

find the range of the function f(x)=x^3-12x over the interval [-1, 3]

Answer 1

differentiate the function... find the stationary points...

this will give a max and min value for the range...

you may need the 2nd derivative to determine the nature of the stationary points..

a simpler method is to us a graphing package and graph the curve then read off the max and min y values over the domain.

Answer 2

don't forget to try the endpoints of the interval as well. you need to check both the zeros of the derivative, and the end points of the interval
the largest is the max, the smallest is the min

Answer 3

how would i write the range (i found the max and min)

Answer 4

and did you check the endpoints...

so the range will be [min, max]

Answer 5

oh that makes sense! thank you so much