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Derivatives - College Paper

Derivatives

1.6 Topics: Using basic differentiation rules. SOLUTIONS

Use the rules of differentiation to find the derivatives. Hint: Rewrite #5 - 7 before differentiating.

1. 2. 3. 4.

5. 6. 7. 8.

9. What is the equation of the line tangent to at the point?

10. At what point(s) will have a horizontal tangent line?

To solve this problem we will take the derivative and set it equal to zero (a horizontal tangent line will have a slope equal to zero).

Note: To get the "y" values for the points just substitute the "x" values into the original equation

11. If what is the relationship between the derivative of and the ...

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rule we know that the derivative of will be times the derivative of .

From a graphical perspective, if then the graph of is a reflection of the graph of about the x - axis and stretched vertically by a factor of three. So for any particular x value, the slope of the tangent line at x on the graph of

will be - 3 times what it was at the same x value on the graph of .

For a free falling object gives the position (in feet) of an object with initial velocity (in feet per second) and initial position where is time (in seconds).

A ball is thrown straight down from the top of a 220 foot building with an initial speed of 22 feet per second.

(Any answers that are not exact please round to two decimal places).

13. What is the velocity of the ball after three seconds?

14. What is it's velocity after falling 108 feet?

To solve this just set the position (s(t)) equal to 108 ft to find out WHEN (what time) this occurs then evaluate v(t) at this value of ...

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Derivatives. (2017, May 3). Retrieved June 29, 2025, from http://www.essayworld.com/essays/Derivatives/106261

"Derivatives." Essayworld.com. Essayworld.com, 3 May. 2017. Web. 29 Jun. 2025. <http://www.essayworld.com/essays/Derivatives/106261>

"Derivatives." Essayworld.com. May 3, 2017. Accessed June 29, 2025. http://www.essayworld.com/essays/Derivatives/106261.

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PAPER DETAILS

Added: 5/3/2017 08:37:16 PM
Submitted By: senioritis
Category: Education
Type: Free Paper
Words: 558
Pages: 3

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