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First Derivative Test Worksheet

A worksheet for Grade 10 students covering the First Derivative Test, including finding critical points, intervals of increase and decrease, and local extrema.

Grade 10 Math CalculusFirst Derivative Test
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Includes

3 Short AnswerFill in the BlanksMultiple ChoiceTrue / False

Standards

CCSS.MATH.CONTENT.HSF.IF.C.7.E

Topics

CalculusFirst Derivative TestDerivativesLocal ExtremaIncreasing/Decreasing Functions
8 sections · Free to use · Printable
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First Derivative Test Worksheet

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Read each question carefully and show all your work. Use the First Derivative Test to determine intervals of increase/decrease and local extrema for the given functions.

1. Find the critical points of the function f(x) = x³ - 6x² + 5.

2. For the function f(x) = x² - 4x + 3, the critical point is x =  .

At this point, the function has a local   (maximum/minimum).

3. Determine the intervals where the function f(x) = x³ - 3x² - 9x + 1 is increasing and decreasing.

-1 3

4. If f'(x) changes from positive to negative at x = c, what does the First Derivative Test imply about f(x) at x = c?

a

Local minimum

b

Local maximum

c

Inflection point

d

No extremum

5. The First Derivative Test can be used to find absolute extrema.

T

True

F

False

6. Analyze the function f(x) = (x - 2)²(x + 1) using the First Derivative Test to find all local extrema.