Question 1

Use a graphing utility to estimate the absolute maximum of  on [2, 10].

Accepted Answer

The answer of Use a graphing utility to estimate the...

Question 2

The strength of a beam with a rectangular cross section varies directly as x and as the square of y. What are the dimensions of the strongest beam that can be sawed out of a round log whose diameter is d = 27 inches? See figure on right.

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The answer of The strength of a beam with a...

Question 3

Use a graphing utility to estimate the absolute maximum of f(x) = x⁵ ln x on [1, 5].

Accepted Answer

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Question 4

Find the point on the curve x² + y² = 64 closest to (7, 0).

Accepted Answer

The answer of Find the point on the curve x²...

Question 5

A rectangular lot is to be bounded by a fence on three sides and by a wall on the fourth side. Two kinds of fencing will be used with heavy duty fencing selling for $4 a foot on the side opposite the wall. The two remaining sides will use standard fencing selling for $3 a foot. What are the dimensions of the rectangular plot of greatest area that can be fenced in at a cost of $25,920?

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Question 6

A divided field is to be constructed with 7640 feet of fence as shown.
For what value of x will the area be a maximum?

Accepted Answer

The answer of A divided field is to be constructed...

Question 7

A long strip of copper 8 inches wide is to be made into a rain gutter by turning up the sides to form a trough with a rectangular cross section. Find the dimensions of the cross section if the carrying capacity of the trough is to be a maximum.

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The answer of A long strip of copper 8 inches...

Question 8

A sheet of cardboard 30 in square is used to make an open box by cutting squares of equal size from the corners and folding up the sides. What size squares should be cut to obtain a box with largest possible volume?

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The answer of A sheet of cardboard 30 in square...

Question 9

Find the point on the curve x² + y² = 36 closest to (0, 8).

Accepted Answer

The answer of Find the point on the curve x²...

Question 10

Find the point on the curve x² + y² = 16 closest to (7, 0).

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The answer of Find the point on the curve x²...

Question 11

Find the area of the largest possible isosceles triangle with 2 sides equal to 12.

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Question 12

Find the dimensions of the rectangle of maximum area which may be embedded in a right triangle with base of 10, height of 24, and hypotenuse of 26 feet as shown in the figure.

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Question 13

Use a graphing utility to estimate the absolute maximum of f(x) = -e²^x on [-3, 3]. at

Accepted Answer

The answer of Use a graphing utility to estimate the...

Question 14

Find the dimensions of the rectangle of greatest area that can be inscribed in a circle of radius a.

Accepted Answer

The answer of Find the dimensions of the rectangle of...

Question 15

Express the number 27 as a sum of two nonnegative terms whose product is as large as possible.

Accepted Answer

The answer of Express the number 27 as a sum...

Question 16

Use a graphing utility to estimate the absolute maximum of  on [-2, 2].

Accepted Answer

The answer of Use a graphing utility to estimate the...

Question 17

Use a graphing utility to estimate the absolute maximum of f(x) = -(ln x)⁸ on [1, 10].

Accepted Answer

The answer of Use a graphing utility to estimate the...

Question 18

The infield of a 440 yard track consists of a rectangle and 2 semicircles. To what dimensions should the track be built in order to maximize the area of the rectangle?

Accepted Answer

The answer of The infield of a 440 yard track...

Question 19

An isosceles triangle is drawn with its vertex at the origin and its base parallel to the x axis. The vertices of the base are on the curve 5y = 25-x². Find the area of the largest such triangle.

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The answer of An isosceles triangle is drawn with its...

Question 20

A lighthouse is 8 miles off a straight coast and a town is located 18 miles down the seacoast. Supplies are to be moved from the town to the lighthouse on a regular basis and at a minimum time. If the supplies can be moved at the rate of 7 miles/hour on water and 25 miles/hour over land, how far from the town should a dock be constructed for shipment of supplies?

Accepted Answer

The answer of A lighthouse is 8 miles off a...

Quiz 4: The Derivative in Graphing and Applications

Use a graphing utility to estimate the absolute maximum of on [2, 10].

The strength of a beam with a rectangular cross section varies directly as x and as the square of y. What are the dimensions of the strongest beam that can be sawed out of a round log whose diameter is d = 27 inches? See figure on right.

Use a graphing utility to estimate the absolute maximum of f(x) = x5 ln x on [1, 5].

Find the point on the curve x2 + y2 = 64 closest to (7, 0).

A divided field is to be constructed with 7640 feet of fence as shown. For what value of x will the area be a maximum?

A long strip of copper 8 inches wide is to be made into a rain gutter by turning up the sides to form a trough with a rectangular cross section. Find the dimensions of the cross section if the carrying capacity of the trough is to be a maximum.

A sheet of cardboard 30 in square is used to make an open box by cutting squares of equal size from the corners and folding up the sides. What size squares should be cut to obtain a box with largest possible volume?

Find the point on the curve x2 + y2 = 36 closest to (0, 8).

Find the point on the curve x2 + y2 = 16 closest to (7, 0).

Find the area of the largest possible isosceles triangle with 2 sides equal to 12.

Find the dimensions of the rectangle of maximum area which may be embedded in a right triangle with base of 10, height of 24, and hypotenuse of 26 feet as shown in the figure.

Use a graphing utility to estimate the absolute maximum of f(x) = -e2x on [-3, 3]. at

Find the dimensions of the rectangle of greatest area that can be inscribed in a circle of radius a.

Express the number 27 as a sum of two nonnegative terms whose product is as large as possible.

Use a graphing utility to estimate the absolute maximum of on [-2, 2].

Use a graphing utility to estimate the absolute maximum of f(x) = -(ln x)8 on [1, 10].

The infield of a 440 yard track consists of a rectangle and 2 semicircles. To what dimensions should the track be built in order to maximize the area of the rectangle?

An isosceles triangle is drawn with its vertex at the origin and its base parallel to the x axis. The vertices of the base are on the curve 5y = 25-x2. Find the area of the largest such triangle.

Use a graphing utility to estimate the absolute maximum of f(x) = x⁵ ln x on [1, 5].

Find the point on the curve x² + y² = 64 closest to (7, 0).

Find the point on the curve x² + y² = 36 closest to (0, 8).

Find the point on the curve x² + y² = 16 closest to (7, 0).

Use a graphing utility to estimate the absolute maximum of f(x) = -e²^x on [-3, 3]. at

Use a graphing utility to estimate the absolute maximum of f(x) = -(ln x)⁸ on [1, 10].

An isosceles triangle is drawn with its vertex at the origin and its base parallel to the x axis. The vertices of the base are on the curve 5y = 25-x². Find the area of the largest such triangle.