Arrival Activity: Put the answers to the following question in your notes. Use complete sentences so that you know what your answers mean when you review.

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Presentation transcript:

Arrival Activity: Put the answers to the following question in your notes. Use complete sentences so that you know what your answers mean when you review. What is average rate of change? What is instantaneous rate of change? What equation can we use to find the slope of the secant line? What is the limit statement that is used to find the slope of a tangent line to a curve? Are the slope of the tangent line to a curve at x=a and the slope of the curve at x=a the same?

Answers Average rate of change is slope between two points. Instantaneous rate of change is slope a specific moment or single point. The slope of the secant line can be found using The limit statement used to find the slope of a tangent line to a curve is 5. Yes, the slope of the tangent line to a curve at x=a and the slope of the curve at x=a are the same.

Derivative 2nd Definition of Derivative Derivative Notation Rules! AP Calculus Unit 2 Day 2 Derivative 2nd Definition of Derivative Derivative Notation Rules!

Yesterday’s Vocabulary Notes Slope of the Tangent Line of f(x): “Slope at a point or specific moment” “Slope of a curve” “Instantaneous rate of change”

Today’s New Vocabulary Derivative of f(x): “Instantaneous Rate of Change of f(x)” “Slope at a point or specific moment” “Slope of a curve” “Slope of the tangent line to the curve”

Checking for Understanding—Good Quiz/Test Type Question What do each of the following limit statements represent?

Today’s New Notation f’(x) : Derivative of f(x) f’’(x) : Second Derivative of f(x) f’(a) : Derivative of f(x) evaluated at a : Derivative of y with respect to x : Second derivative of y with respect to x

Alternative Limit Definition of a Derivative is the slope of the secant line is the slope of the tangent line, slope of curve at x=a, derivative of f(x) at x=a

Derivative of a Constant f(x) = 6 y = -20 f(x) = 1203

Derivative of a Linear Function f(x) = ½ x - 3 y = -3x + 4

The Power Rule

Practice:

What observation can you make about the degree of the function and the degree of its derivatives?

Miscellanous Odds and Ends Vocabulary: Differentiable—(Adjective) Capable of being differentiated Differentiate—(Verb) To obtain the derivative

Deep Thoughts At what point on the graph of y = 2x2 is the tangent line parallel to the line 6x + 3y = 4?