# calculus

posted by .

find the absolute minimum and maximum values of f(x)=x^(1/3) (3+x) on the interval [-2,1]

• calculus -

f' = (4x+3)/(3x^(2/3))
This is undefined at x=0, where f(0) = 0, a local min.

f'=0 at x = -3/4 where there is a local max. f(-3/4) = -(9/4) ∛(3/4)

check the value of f at the end points for other max/min values.

• calculus -

do not get it :(

• calculus -

what don't you get?
max/min occurs where f' = 0, as long as f" is not also zero

where f' is undefined, check to see whether f is defined there. If so, it will be some kind of cusp, so a max or min. Or it will have a vertical tangent.

As it turns out, I made a mistake at x=0; there is no local min there.
And, the extremum at x = -3/4 is a min, not a max.

Oddly, this error was caused by my trust in the graphs at wolframalpha.com, which showed it wrong.

To see the real graph, visit

http://rechneronline.de/function-graphs/

## Similar Questions

1. ### Calculus

Find the absolute maximum and absolute minimum values of f(x)=sinx + (ã3) cosx on the closed interval [0,ƒÎ/3]
2. ### 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 …
3. ### 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 …
4. ### Calculus

Find the absolute maximum and absolute minimum values of the function f(x)=x^3+6x^2-63x+4 on each of the indicated variables. Enter DNE for does not exist. (A) Interval = [-8,0] Absolute maximum = Absolute minimum = (B) Interval = …
5. ### Calculus

Find the absolute minimum and absolute maximum values of f on the interval below. f(x) = x4 - 8x2 + 6 [-3, 4]
6. ### Calculus

Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = (x2 - 1)3 [-1, 6]
7. ### Calculus

Find the absolute minimum and absolute maximum values of f on the given interval. f(t) = 8 cos t + 4 sin 2t, [0, π/2]
8. ### calculus

2) Let g(s)= t(4−t)^1/2 on the interval [0,2]. Find the absolute maximum and absolute minimum of g(t) on this interval. Enter DNE if the absolute maximum or minimum does not exist. The absolute max occurs at t= . The absolute …
9. ### Calculus 1

Find the absolute maximum and absolute minimum values of f on the given interval. f(x)=(x^2-4)/(x^2+4), [-4,4]
10. ### Calculus 1

Find the absolute minimum and absolute maximum values of f on the given interval. f(t) = 16 cos t + 8 sin 2t, [0, π/2]

More Similar Questions