Warm Up #3 Sept. 1st. Derivatives & differentiation IB MATH STUDIES 2 SEPTEMBER 1 ST, 2015.

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Presentation transcript:

Warm Up #3 Sept. 1st

Derivatives & differentiation IB MATH STUDIES 2 SEPTEMBER 1 ST, 2015

 How can we adapt this idea to define the gradient of a curve?  Using GDC or math software you can graph a curve and zoom in to a small section, the more you zoom, the more the curve looks like a straight line!

Finding the gradient of a curve at a point The gradient is different at every point on the curve. For example: When x = -2.5, the curve is decreasing steeply—the gradient is negative and large As x increases towards zero, the gradient remains negative but becomes smaller in magnitude (the curve becomes less steep) The curve is flat at (0,0) which means here the gradient is zero As x increases from 0, the curve slopes upward and gets steeper—the gradient is positive and getting larger

Tangents to Curves

Limits

Limit Examples

Practice finding limits!

The Derivative Function

Derivative Function

Derivative Example

Find the derivative using the definition….

Shortcut!

Examples from before the rule-

Rules of Differentiation

Example

 In examinations, several different instructions may be used that all mean find the derivative! InstructionExample FunctionExample Answer Find f’(x) Differentiate with respect to x Find the gradient function Find the derivative of the function

Finding the gradient when x = …  When asked to find the gradient at a certain point, take the derivative & plug in the value!

a) Find dy/dx b) Copy and complete the table below c) What is the gradient of the curve at x = 2? d) Use the table to sketch the curve X0123 Y dy/dx

Example

Homework  Read pages 572 – 588 in your textbook!  Be able to tell me at least one piece of interesting information that you learned in the text (that we had not learned in the lesson!)  PG. 581 Exercises 20.1 (all)  PG Exercises 20.2 (all)