Question 1

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The answer of 
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Question 2

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The answer of 
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Question 3

If an object moves along a line so that it is at y = f(x) = 10x² at time x (in seconds), find the velocity at x =1 (y is measured in feet).

Accepted Answer

The velocity is the derivative of the position function. The derivative of f(x) = 10x² is f'(x) = 20x. At x = 1, the velocity is f'(1) = 20(1) = 20 ft/s.

Question 4

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Question 5

Find f'(x) for f(x) =

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Question 6

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Question 7

Suppose an object moves along the y-axis so that its location is y = f(x) = x² + x at time x (y is in meters and x is in seconds). Find the instantaneous velocity at x = 4 seconds.

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Question 8

If an object moves along a line so that it is at y = f(x) =  at time x (in seconds), find the instantaneous velocity function v = f'(x).

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The answer of If an object moves along a line...

Question 9

Accepted Answer

The last number in the given code is "2" which is the check digit. To calculate the check digit, we need to add all the other digits and take the remainder when divided by 10. 
In this case, (1+1+0+8+7+7+2+7+5+5+1+8+1+3+9+2+0+0) = 58. 
The remainder when this is divided by 10 is 8. Therefore, the check digit should be equal to 10 - 8 = 2 (as it is). 
This means all the other digits must be correct. So the answer is C, which is -15.

Question 10

Find f'(x) if f(x) =

Accepted Answer

The answer of Find f'(x) if f(x) = 
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Question 11

Suppose an object moves along the y-axis so that its location is y = f(x)= x² + x at time x (y is in meters and x is in seconds). Find the average veloity for x changing from 3to 3 + h seconds.

Accepted Answer

The average velocity is given by the change in position over the change in time. For x changing from 3 to 3 + h, the average velocity is [f(3 + h) - f(3)] / h. Calculating f(3) = 3² + 3 = 12 and f(3 + h) = (3 + h)² + (3 + h) = 9 + 6h + h² + 3 + h = 12 + 7h + h². The change in position is (12 + 7h + h²) - 12 = 7h + h². Dividing by h gives (7h + h²)/h = 7 + h. Thus, the average velocity is 7 + h m/s.

Question 12

Find y' if y = 6x.

Accepted Answer

The answer of Find y' if y = 6x....

Question 13

Suppose an object moves along the y-axis so that its location is y = f(x) = at time x (y is in meters and x is in seconds). Find the average velocity (the average rate of change of y with respect to x) for x changing from 2 to 9 seconds.

Accepted Answer

To find the average velocity, we need to find the change in y (Δy) divided by the change in x (Δx) between 2 and 9 seconds.

Δy = f(9) - f(2) = 11ec60b8_7c96_a937_b81b_cf149748b8d5_TB34225555_11 - 11ec60b8_7c96_a937_b81b_cf149748b8d5_TB342246437_11 = 430.27 meters

Δx = 9 - 2 = 7 seconds

Average velocity = Δy/Δx = 430.27/7 ≈ 61.47 m/s

Therefore, the closest choice is B) 12m/s.

Question 14

The electric power p (in W) as a function of the current i (in A) in a certain circuit is given by p(i) = .
Find the instantaneous rate of change of p with respect to i for i = 0.6 A.

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Question 15

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Question 16

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Question 17

Find f'(x) if

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Question 18

Let f and g be functions that satisfy f'(4)= 2 and g'(4)= -3.Find h'(4)for h(x)= 3f(x)- g(x)+ 2.

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The answer of Let f and g be functions that...

Question 19

Find f'(x) if f(x) =n.

Accepted Answer

The derivative of a constant function is always 0.

Question 20

Find the derivative of

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The answer of Find the derivative of 
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Quiz 11: Mathematical Functions and Limits

If an object moves along a line so that it is at y = f(x) = 10x² at time x (in seconds) , find the velocity at x =1 (y is measured in feet) .

Find f'(x) for f(x) =

Suppose an object moves along the y-axis so that its location is y = f(x) = x² + x at time x (y is in meters and x is in seconds) . Find the instantaneous velocity at x = 4 seconds.

If an object moves along a line so that it is at y = f(x) = at time x (in seconds) , find the instantaneous velocity function v = f'(x) .

Find f'(x) if f(x) =

Suppose an object moves along the y-axis so that its location is y = f(x) = x² + x at time x (y is in meters and x is in seconds) . Find the average veloity for x changing from 3to 3 + h seconds.

Find y' if y = 6x.

Suppose an object moves along the y-axis so that its location is y = f(x) = at time x (y is in meters and x is in seconds) . Find the average velocity (the average rate of change of y with respect to x) for x changing from 2 to 9 seconds.

The electric power p (in W) as a function of the current i (in A) in a certain circuit is given by p(i) = . Find the instantaneous rate of change of p with respect to i for i = 0.6 A.

Find f'(x) if

Let f and g be functions that satisfy f'(4) = 2 and g'(4) = -3.Find h'(4) for h(x) = 3f(x) - g(x) + 2.

Find f'(x) if f(x) =n.

Find the derivative of