Application of Differentiation: Maximum and Minimum Values Quiz

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What is the point on the parabola 𝑦 = 9 − 𝑥^2 closest to the point 𝐴(3,9)?

(5,2)

(2,5)

(1,8) (correct)

(4,3)

You are inflating a spherical balloon at the rate of 32 cm³/sec. How fast, in cm/sec, is its radius increasing when the radius is 4 cm?

2 cm/sec

4 cm/sec (correct)

6 cm/sec

8 cm/sec

An airplane is flying away from a radar station at a constant height of 8 miles above the ground. If the distance s between the airplane and the station is increasing at a rate of 300 miles per hour when s = 10 miles, what is the horizontal speed, in miles per hour, of the plane?

375 mph (correct)

500 mph

300 mph

250 mph

Suppose a forest fire spreads in a circle with radius changing at a rate of 8 ft/min. When the radius reaches 200 feet, at what rate is the area of the burning region increasing?

3200π ft²/min Signup and view all the answers

A gas is poured into a spherical balloon at a constant rate of 15 cm³/sec. At what rate is the radius of the balloon increasing when the radius is 8 cm?

0.019 cm/sec Signup and view all the answers

A cylindrical tank with radius 5 m is being filled with water at a rate of 3 m³/min. How fast is the height of the water increasing?

$\frac{3}{5}$ m/min Signup and view all the answers

The length of a rectangle is increasing at a rate of 6 cm/sec and its width is increasing at a rate of 2 cm/sec. When the length is 18 cm and the width is 10 cm, how fast is the area of the rectangle increasing?

$120$ cm²/sec Signup and view all the answers

If the volume of a sphere is decreasing at the rate of 20 cm³/sec, find the rate at which the radius of the sphere is decreasing when the volume is 8 cm³.

$2$ cm/sec Signup and view all the answers

What are the critical points of the function $f(x) = -16x$?

$x = -2$ and $x = 2$ Signup and view all the answers

At which value(s) of $x$ does the function $g(x) = 2x^3 - 4x$ have critical point(s)?

$x=0$ Signup and view all the answers

What is the absolute maximum value of the function $y = -x^2 + 5x + 6$ on the interval $[2, 15]$?

$y=12.25$ Signup and view all the answers

What is the absolute minimum value of the function $y = 2 \sin x$ on the interval $[0, 6.2]$?

$y=1.5$ Signup and view all the answers

Application of Differentiation: Maximum and Minimum Values Quiz

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Questions and Answers

What is the point on the parabola 𝑦 = 9 − 𝑥^2 closest to the point 𝐴(3,9)?

You are inflating a spherical balloon at the rate of 32 cm³/sec. How fast, in cm/sec, is its radius increasing when the radius is 4 cm?

An airplane is flying away from a radar station at a constant height of 8 miles above the ground. If the distance s between the airplane and the station is increasing at a rate of 300 miles per hour when s = 10 miles, what is the horizontal speed, in miles per hour, of the plane?

Suppose a forest fire spreads in a circle with radius changing at a rate of 8 ft/min. When the radius reaches 200 feet, at what rate is the area of the burning region increasing?

A gas is poured into a spherical balloon at a constant rate of 15 cm³/sec. At what rate is the radius of the balloon increasing when the radius is 8 cm?

A cylindrical tank with radius 5 m is being filled with water at a rate of 3 m³/min. How fast is the height of the water increasing?

The length of a rectangle is increasing at a rate of 6 cm/sec and its width is increasing at a rate of 2 cm/sec. When the length is 18 cm and the width is 10 cm, how fast is the area of the rectangle increasing?

If the volume of a sphere is decreasing at the rate of 20 cm³/sec, find the rate at which the radius of the sphere is decreasing when the volume is 8 cm³.

What are the critical points of the function $f(x) = -16x$?

At which value(s) of $x$ does the function $g(x) = 2x^3 - 4x$ have critical point(s)?

What is the absolute maximum value of the function $y = -x^2 + 5x + 6$ on the interval $[2, 15]$?

What is the absolute minimum value of the function $y = 2 \sin x$ on the interval $[0, 6.2]$?

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