Find (withoutusing a calculator) the absolute extreme values of the function on the given interval.

f(x) =x³9x²+15x+7on [1, 2]

absolute min
absolute max

2.

Find (withoutusing a calculator) the absolute extreme values of the function on the given interval.

f(x) =x⁴+ 4x³+17

on

[4, 1]

absolute min
absolute max

3.

Find (withoutusing a calculator) the absolute extreme values of the function on the given interval.

f(x) =x²(6x) on [1,6]

absolute min
absolute max

4.

Find (withoutusing a calculator) the absolute extreme values of the function on the given interval.

f(x) =

x

x²+1

on [3,3]

absolute min
absolute max

5.

Find the number in the interval [0,7] such that the number minus its square is as follows.(a) as large as possible (b) as small as possible

6.

The fuel economy (in miles per gallon) of a certain car is

E(x) =0.01x²+0.52x+10.4,

wherexis the driving speed (in miles per hour,

20x60).

At what speed is fuel economy greatest?

x= mph

7.

Two chemical factories are discharging toxic waste into a large lake, and the pollution level at a pointxmiles from factory A toward factory B is

P(x) =3x²72x+540

parts per million

(for 0x50).

Find where the pollution is the least.

x= mi

8.

A real estate company wants to build a parking lot along the side of one of its buildings using500feet of fence. If the side along the building needs no fence, what are the dimensions (in ft) of the largest possible parking lot?

A rectangular parking lot has been enclosed along a side of a building. The enclosure is bordered by the building (a long side), another long side of fence, and two short sides of fence.

side parallel to the building ftside perpendicular to the building ft

9.

What is the difference between anabsolutemaximum value and arelativemaximum value? A function can have at most one relative maximum value, but it can have several absolute maximum values.If a function has several relative maximum values, then it cannot have an absolute maximum value. The absolute maximum value of a function must be greater than the relative maximum value.The relative maximum value of a function must be greater than the absolute maximum value.A function can have at most one absolute maximum value, but it can have several relative maximum values.

10.

If

f'(1) = 0

and

f''(1) > 0,

what conclusion can you draw? There is a relative minimum atx= 1.There is a relative maximum atx= 1. There is an absolute minimum atx= 1.There is an absolute maximum atx= 1.none of these