calculus

find the maximum and minimum value of the function f(x)= x-x^3 on the interval [-2,2]


I also need help with this question

What is the largest possible product of two negative number whose sum is 1?

asked by jake
  1. check end points
    f(-2) = -2+8 = 6
    f(2) = 2-8 = -6

    now find where derivative is zero
    f' = 1 -3x^2
    = 0 when x = 1/sqrt3 or x = -1/sqrt3

    if x = 1/sqrt 3
    f = 1/sqrt3 -1/3sqrt3 =(2/3sqrt3)

    if x = -1/sqrt3
    f = -1/sqrt3 +1/3sqrt 3
    = -(2/3sqrt3)
    so the max and min are at the end points max at -2 and min at +2

    posted by Damon

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