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Introduction to Derivatives

Explore the fundamental concepts of derivatives, including limits, slopes of tangent lines, and basic differentiation rules.

Grade 9 Math CalculusDerivatives
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Includes

Multiple ChoiceFill in the Blanks2 Short AnswerTrue / False

Standards

CCSS.MATH.CONTENT.HSF.IF.B.4CCSS.MATH.CONTENT.HSF.IF.B.6

Topics

CalculusDerivativesGrade 9Math
7 sections · Free to use · Printable
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Introduction to Derivatives

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Read each question carefully and answer to the best of your ability. Show all your work for full credit.

1. What does the derivative of a function represent graphically?

a

The area under the curve

b

The slope of the tangent line

c

The y-intercept of the function

d

The x-intercepts of the function

2. The process of finding the derivative of a function is called:

a

Integration

b

Differentiation

c

Factorization

d

Simplification

3. The derivative of a constant function is always  .

4. The power rule states that if f(x) = x^n, then f'(x) =  .

5. Explain in your own words what a limit is in the context of calculus.

6. The derivative of f(x) = 3x is 3.

T

True

F

False

7. A function must be continuous at a point to be differentiable at that point.

T

True

F

False

8. Find the derivative of the function f(x) = 5x^3 - 2x + 7 using the power rule.