Jessica

posted by .

Find absolute maximum and minimum for f(x)=(3x^3)−(18x^2)+27x−10 over the closed interval [2,4].


Thank you so much!!

  • Jessica -

    f = 3x^3−18x^2+27x−10
    f' = 9x^2 - 36x + 27 = 9(x^2-4x+3) = 9(x-1)(x-3)

    so, f has a relative min/max at x=3
    From what you know about the general shape of cubics, it should be clear that (3,-10) is a relative min.

    since
    f(2) = -4
    f(4) = 2,

    f(3) = -10 is the absolute min within the interval
    f(4) = 2 is the absolute max in the interval

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. 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 …
  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. math calculus

    Find the absolute extrema of the function on the closed interval. Use a graphing utility to verify your results. (Round your answers to two decimal places. If an answer does not exist, enter DNE.) g(x) = (x^2 − 4)^2/3, [−5, …
  4. calculus

    Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = e−x − e−7x, [0, 1]
  5. Calculus Help Please!!!

    Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 2x^3 − 3x^2 − 72x + 7 , [−4, 5]
  6. Calculus Help Please!!!

    Find the absolute maximum and absolute minimum values of f on the given interval. f(t) = (t square root of (64 − t^2)), [−1, 8]
  7. Calculus Help Please!!!

    Find the absolute maximum and absolute minimum values of f on the given interval. f(t) = (t square root of (64 − t^2)) ,[−1,8]
  8. Calculus Help Please!!!

    Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = xe^((−x^2)/98), [−6, 14]
  9. Calculus 1

    Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = (e^−x)*(− e^−6x), [0, 1]
  10. 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) …

More Similar Questions