1. Find the absolute minimum and absolute maximum values of f on the given interval. f(x) = ((x^2) − 1)^3, [−1, 4] absolute minimum( ) absolute maximum( ) 2. Find the absolute maximum and
Please write down the detail step and correct answer, thanks a lot.
1. Find the absolute minimum and absolute maximum values of f on the given interval.
f(x) = (x2 − 1)3, [−1, 4]
absolute minimum=
absolute maximum=
2. Find the absolute maximum and absolute minimum values of f on the given interval.
f(t) = 2 cos(t) + sin(2t), [0, π/2]
absolute minimum=
absolute maximum=
3.Find the absolute minimum and absolute maximum values of f on the given interval.
f(t) = 3t + 3 cot(t/2),
[π/4, 7π/4]
| absolute minimum value | = |
absolute maximum value=
4.Find the absolute maximum and absolute minimum values of f on the given interval.
f(t) = t√64-t^2 [−1, 8]
| absolute minimum value | = |
absolute maximum value=
5.Find the absolute maximum and absolute minimum values of f on the given interval.
f(x) = xe−x2/72,
[−5, 12]
| absolute minimum value | = |
absolute maximum value=
6.Find the absolute minimum and absolute maximum values of f on the given interval.
f(x) = x − ln(2x), [1/2,2]
absolute minimum=
absolute maximum=
Find the dimensions of a rectangle with perimeter 84 m whose area is as large as possible. (If both values are the same number, enter it into both blanks.)
( )m (smaller value)
( )m (larger value)
Find the dimensions of a rectangle with area 1,000 m2 whose perimeter is as small as possible. (If both values are the same number, enter it into both blanks.)
( )m (smaller value)
( )m (larger value)
9.A model used for the yield Y of an agricultural crop as a function of the nitrogen level N in the soil (measured in appropriate units) is
Y =
| kN |
| 9 + N2 |
where k is a positive constant. What nitrogen level gives the best yield?
N=
10.The rate (in mg carbon/m3/h) at which photosynthesis takes place for a species of phytoplankton is modeled by the function
P =
| 120I |
| I2 + I + 4 |
where I is the light intensity (measured in thousands of foot-candles). For what light intensity is P a maximum?
I= thousand foot-candles
Consider the following problem: A box with an open top is to be constructed from a square piece of cardboard, 3 ft wide, by cutting out a square from each of the four corners and bending up the sides. Find the largest volume that such a box can have.
Finish solving the problem by finding the largest volume that such a box can have.
V= ( )ft^3
A box with a square base and open top must have a volume of 4,000 cm3. Find the dimensions of the box that minimize the amount of material used.
| sides of base | =( )cm |
height =( )cm
If 1,200 cm2 of material is available to make a box with a square base and an open top, find the largest possible volume of the box.
( )cm^3
13.(a) Use Newton's method with x1 = 1 to find the root of the equation
x3 − x = 4
correct to six decimal places.
x =
(b) Solve the equation in part (a) using x1 = 0.6 as the initial approximation.
x =
(c) Solve the equation in part (a) using x1 = 0.57. (You definitely need a programmable calculator for this part.)
x =
14.Use Newton's method to find all roots of the equation correct to six decimal places. (Enter your answers as a comma-separated list.)
3 cos x = x + 1
x =
15.Use Newton's method to find all roots of the equation correct to six decimal places. (Enter your answers as a comma-separated list.)
(x − 5)2 = ln(x)
x =
16.Use Newton's method to find all real roots of the equation correct to six decimal places. (Enter your answers as a comma-separated list.)
| 8 |
| x |
= 1 + x3
x=
17.A particle is moving with the given data. Find the position of the particle.
v(t) = 1.5* sqrt(t), s(4) = 13
s(t) =
18. Find f.
f ''(θ) = sin(θ) + cos(θ), f(0) = 2, f '(0) = 3
f(θ) =
19. Find f.
f ''(x) = 4 + cos(x), f(0) = −1, f(7π/2) = 0
f(x)=
20.Find f.
f ''(t) = 3et + 8 sin(t), f(0) = 0, f(π) = 0 f(t)=
