# calculus

posted by jake

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?

1. Damon

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

## Similar Questions

1. ### Calculus

Find the sum of two numbers whose sum is 70 and whose product is as large as possible. Ok i got that one equation is y = 70 - x...but how do I show an equation for a product which is as large as possible. The product is P = x (70 - …

A continuous function f, defined for all x, has the following properties: 1. f is increasing 2. f is concave down 3. f(13)=3 4. f'(13)=1/4 Sketch a possible graph for f, and use it to answer the following questions about f. A. For …

A continuous function f, defined for all x, has the following properties: 1. f is increasing 2. f is concave down 3. f(13)=3 4. f'(13)=1/4 Sketch a possible graph for f, and use it to answer the following questions about f. A. For …
4. ### Calculus (pleas help!!!)

Find the absolute maximum and absolute minimum values of the function f(x)=(x−2)(x−5)^3+11 on each of the indicated intervals. Enter -1000 for any absolute extrema that does not exist. (A) Interval = [1,4] Absolute maximum …
5. ### Calculus (pleas help!!!)

Find the absolute maximum and absolute minimum values of the function f(x)=(x−2)(x−5)^3+11 on each of the indicated intervals. Enter -1000 for any absolute extrema that does not exist. (A) Interval = [1,4] Absolute maximum …
6. ### calculus

Find the absolute extrema of the function (if any exist) on each interval. (If an answer does not exist, enter DNE.) f(x) = square root of (25 − x^2) (a) [−5, 5] minimum (x, y) = (smaller x-value) (x, y) = (larger x-value) …