# calculus

posted by .

find the absolute minimum and maximum valies of f(x)=-x^4+2x^3+5 on the interval [-2,2]

• calculus -

check f(-2) and f(2).

f' = -4x^3 + 6x^2
= -2x^2(2x-3)
so there are local extrema at x = 3/2
Not at x=0, since that's a double root of f'=0.

Now pick the max/min values of f at -2,3/2,2

• calculus -

f ' (x) = - 4x^3 + 6x^2
= 0 for max/min

x^2(-4x + 6) = 0
x = 0 or x = 3/2

f(0) = 5
f(3/2) = -81/64 + 54/8 + 5 = 671/64 = appr 10.48
f(-2) = - 16 + 16 + 5 = 5
f(2) = -16 - 16 + 5 = -27

so the absolute max is 671/64 and the min is -27

## 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. ### Calculus

Find the absolute extrema of the function on the interval [2, 9]. (Round your answers to the nearest hundredth.) g(x)=x/(ln(x)) Absolute minimum: at x = Absolute maximum: at x =
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

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 …
6. ### calculus

Let f(x)=-x^2+3x on the interval [1,3]. Find the absolute maximum and absolute minimum of f(x) on this interval. The absolute max occurs at x=. The absolute min occurs at x=
7. ### calculus

Let g(s)=1/(s-2) on the interval [0,1]. Find the absolute maximum and absolute minimum of g(s) on this interval. The absolute max occurs at s=. The absolute min occurs at s=
8. ### Calculus

Let f(t)=t\sqrt{4-t} on the interval [-1,3]. Find the absolute maximum and absolute minimum of f(t) on this interval. The absolute max occurs at t=. The absolute min occurs at t=
9. ### calculus

Let g(x)=(4x)/(x^2+1) on the interval [-4,0]. Find the absolute maximum and absolute minimum of g(x) on this interval. The absolute max occurs at x=. The absolute min occurs at x=
10. ### Caluclus

Find the absolute maximum and absolute minimum of f on the interval (-1,2]: f(x)=(-x^3+x^2+3x+1)/(x+1) A. Maximum: (1, -2); Minimum: (-1, 2) B. Maximum: (1, -2); Minimum: None C. Maximum: None; Minimum: None D. Maximum: None; Minimum: …

More Similar Questions