(a) Answer The numbers are 2 and 7 . Explanation The required two number can be select randomly between the 1 and 10. Suppose selected numbers are 2 and 7 . Therefore, the numbers are 2 and 7 . (b) To determine To find: the graph of the obtained equation. Answer The required graph is shown below. Explanation Given: The general equation is y = ( x − a ) ( x + b ) . As the two selected numbers are 2 and 7 . Substitute 2 for x and 7 for y in the equation y = ( x − a ) ( x + b ) . y = ( x − 2 ) ( x + 7 ) Sketch the graph of the equation y = ( x − 2 ) ( x + 7 ) . Therefore, the required graph is shown above. (c) To determine To find: the graph of the derivative of the function. Answer The required graph is shown below. Explanation Given: The function is y = ( x − 2 ) ( x + 7 ) . Consider the function. y = ( x − 2 ) ( x + 7 ) Differentiate the function with respect to x . y = x 2 + 7 x − 2 x − 14 d y d x = d d x [ x 2 + 7 x − 2 x − 14 ] = 2 x Graph of the equation is drawn as, Therefore, the required graph is shown above. (d) To determine To find: the y intercept of the graph. Answer The y intercept is 5 . Explanation Given: The function is y = ( x − 2 ) ( x + 7 ) . Consider the graph. As it is clear from the graph that the graph of derivative of the function cuts the vertical line 5 units . So, the y intercept is 5 . Therefore, the y intercept is 5 . (e) To determine To find: a simple way to predict the y intercept. Answer The simple way to find the y intercept is ( − a + b ) . Explanation Given: The function is y = ( x − a ) ( x + b ) . Consider the function. Expand the function with algebraic properties. y = x 2 − a x + b x + a b = x 2 + x ( − a + b ) + a b Here, ( − a + b ) is the simplest way to find the y intercept. Substitute 2 for a and 7 for b in the equation ( − a + b ) . ( − a + b ) = − 2 + 7 = 5 So, result is verified. Therefore, the simple way to find the y intercept is ( − a + b ) .

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

4th Edition

ISBN: 9780133178579

Author: Ross L. Finney

Publisher: PEARSON

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Question

Chapter 3.1, Problem 43E

(a)

To determine

To find: the two number from 1 to 10.

(a)

Expert Solution

Answer to Problem 43E

The numbers are 2 and 7 .

Explanation of Solution

The required two number can be select randomly between the 1 and 10.

Suppose selected numbers are 2 and 7 .

Therefore, the numbers are 2 and 7 .

(b)

To determine

To find: the graph of the obtained equation.

(b)

Expert Solution

Answer to Problem 43E

The required graph is shown below.

Explanation of Solution

Given:

The general equation is y=(x−a)(x+b) .

As the two selected numbers are 2 and 7 .

Substitute 2 for x and 7 for y in the equation y=(x−a)(x+b) .

y=(x−2)(x+7)

Sketch the graph of the equation y=(x−2)(x+7) .

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy), Chapter 3.1, Problem 43E , additional homework tip 1

Therefore, the required graph is shown above.

(c)

To determine

To find: the graph of the derivative of the function.

(c)

Expert Solution

Answer to Problem 43E

The required graph is shown below.

Explanation of Solution

Given:

The function is y=(x−2)(x+7) .

Consider the function.

y=(x−2)(x+7)

Differentiate the function with respect to x .

y=x2+7x−2x−14dydx=ddx[x2+7x−2x−14]=2x

Graph of the equation is drawn as,

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy), Chapter 3.1, Problem 43E , additional homework tip 2

Therefore, the required graph is shown above.

(d)

To determine

To find: the y intercept of the graph.

(d)

Expert Solution

Answer to Problem 43E

The y intercept is 5 .

Explanation of Solution

Given:

The function is y=(x−2)(x+7) .

Consider the graph.

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy), Chapter 3.1, Problem 43E , additional homework tip 3

As it is clear from the graph that the graph of derivative of the function cuts the vertical line 5 units . So, the y intercept is 5 .

Therefore, the y intercept is 5 .

(e)

To determine

To find: a simple way to predict the y intercept.

(e)

Expert Solution

Answer to Problem 43E

The simple way to find the y intercept is (−a+b) .

Explanation of Solution

Given:

The function is y=(x−a)(x+b) .

Consider the function.

Expand the function with algebraic properties.

y=x2−ax+bx+ab=x2+x(−a+b)+ab

Here, (−a+b) is the simplest way to find the y intercept.

Substitute 2 for a and 7 for b in the equation (−a+b) .

(−a+b)=−2+7=5

So, result is verified.

Therefore, the simple way to find the y intercept is (−a+b) .

Chapter 3.1, Problem 42E

Chapter 3.1, Problem 44E

Chapter 3 Solutions

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

Ch. 3.1 - Prob. 1QR Ch. 3.1 - Prob. 2QR Ch. 3.1 - Prob. 3QR Ch. 3.1 - Prob. 4QR Ch. 3.1 - Prob. 5QR Ch. 3.1 - Prob. 6QR Ch. 3.1 - Prob. 7QR Ch. 3.1 - Prob. 8QR Ch. 3.1 - Prob. 9QR Ch. 3.1 - Prob. 10QR

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