Central Bucks School District
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Save the document as “Your Last Name Making Connections with Derivatives.”
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Calculus I Name:
Understanding the First Derivative
1) Using a website, graph a 3rd degree polynomial (no coefficients of 0) with the general shape of one of the two example graphs to the right.
Equation:
2) Using your graphing calculator, solve for the maximum and minimum points of your graph.
Maximum: Minimum:
3) Take the derivative of the original function. Derivative :
4) Using your graphing calculator, find the zeros of the derivative.
x = b. x =
5) Have you seen these x values before? If so where?
6) Find the equation of the tangent line at the following x-value. (Hint: you will need a slope & a point)
a. x =-2.5
b. x = -1
c. x = 0
d. x = 1.5
e. x = the 1st x-value from #4
f. x = the 2nd x-value from #4
7) Using the website, graph the original equation and copy and paste it below. (you can use prtsc key to copy them and then the crop feature in word) Label it as “the original function.” Then graph the original equation and the 1st tangent line. Copy and paste it below and label it as “a. y = mx + b” filling in the appropriate values for m and b. Repeat for each tangent line. You should have 7 graphs total (1 original, and 6 original with a tangent line).
PASTE GRAPHS HERE
Answer the following questions after completing and analyzing your results.
8) When you find the zeros of the derivative, the values you find are of the original function.
9) When you plug in an x-value to the derivative, you are solving for the of the original function?
10) When the derivative has a positive y-value, then the original function is .
11) When the derivative has a negative y-value, then the original function is .
12) When the derivative’s y-value is zero, then the original function is .
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2 Examples
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