calculas

posted by .

Consider the function f(x)x^4 -32x^2 +2, -3 < or = to x < or = to 9. This function has an absolute minimum value equal to ? and an absolute maximum value equal to ?

  • calculas -

    do the first derivative, set equal to zero.

    Then at each zero, test the second derivative.

    Post back if you are lost.

  • calculas -

    As in the previous problem (quadratic), you will need to first find f'(x).
    Equate f'(x) to zero and solve for the roots. Even f'(x)=0 is a cubic equation, you can easily solve for the three roots by factorization.

    Two of the three roots fall within the given interval, so there is one maximum and one minimum, which you can check by evaluating f"(x). F"(x)>0 is a minimum and f"(x)<0 is a maximum.

    Evaluate f(x) at the two limits of the interval, as well as at the roots of f'(x)=0. These four values will give the absolute maximum and absolute minimum within the interval.

    Post your answers for checking if you wish.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calculus

    Consider the function f(x)=2x3+18x2–240x+3–10x5. This function has an absolute minimum value equal to and an absolute maximum value equal to
  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

    Consider the function f(x)=(x^3)(e^9x), -2 is less than or equal to x is less than or equal to 4 *The absolute maximum value is _____ and this occurs at x equals 4. *The absolute minimum value is _____ and this occurs at x equals ______ …
  5. Calculus

    Find the absolute extrema of the function. (Round your answer to three decimal places.) f(x) = xe-x2 on [0,2] Absolute maximum value: at x = Absolute minimum value: at x =
  6. Calculus

    Find the absolute extrema of the function. (Round your answer to three decimal places.) f(x) = xe^-x2 on [0,2] Absolute maximum value: at x = Absolute minimum value: at x =
  7. Calculus

    Consider the function f(x) = x^4 - 72 x^2 + 3, -5 less than or equal to x less than or equal to 13. This function has an absolute minimum value equal to and an absolute maximum value to
  8. calculas

    Consider the function f(x) = 7 xe^{-7.5 x}, 0<_x<_2. This function has an absolute minimum value equal to: which is attained at x=
  9. calculus

    Consider the function f(x) = x^4 - 18 x^2 + 4, \quad -2 \leq x \leq 7. This function has an absolute minimum value equal to and an absolute maximum value equal to
  10. Math(Calculus)

    Im having a real difficult time solving this question. Find the absolute extrema of the function. h(x) = e^x^(2) - 4 on [-2,2] Absolute maximum value: at x = Absolute minimum value: at x =

More Similar Questions