3.7 Implicit Differentiation

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# 3.7 Implicit Differentiation - PowerPoint PPT Presentation

3.7 Implicit Differentiation. Niagara Falls, NY & Canada. Photo by Vickie Kelly, 2003. Greg Kelly, Hanford High School, Richland, Washington. F4. F3. 2. On the sending unit, press , and then . . 2nd. VAR-LINK. 2nd.

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## 3.7 Implicit Differentiation

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Presentation Transcript
1. 3.7 Implicit Differentiation Niagara Falls, NY & Canada Photo by Vickie Kelly, 2003 Greg Kelly, Hanford High School, Richland, Washington

2. F4 F3 2. On the sending unit, press , and then . 2nd VAR-LINK 2nd F7 Press to select . Calculus Tools 3. On the receiving unit, press . 2nd VAR-LINK 4. On both units, press (Link). 4. On the receiving unit, select (Receive). 2 5. On the sending unit, select (Send). 1 Before we start, we are going to load the Calculus Tools flash application software to your calculator. 1. Connect the sending and receiving calculators together.

3. This is not a function, but it would still be nice to be able to find the slope. Do the same thing to both sides. Note use of chain rule.

4. 1 Differentiate both sides w.r.t. x. 2 Solve for . This can’t be solved for y. This technique is called implicit differentiation.

5. We need the slope. Since we can’t solve for y, we use implicit differentiation to solve for . Find the equations of the lines tangent and normal to the curve at . Note product rule.

6. Find the equations of the lines tangent and normal to the curve at . tangent: normal:

7. Find if . Substitute back into the equation. Higher Order Derivatives

8. Find . APPS ENTER ENTER APPS Select and press . Calculus Tools If you see this screen, press , change the mode settings as necessary, and press again. Now let’s do one on the TI-89:

9. F2 APPS ENTER ENTER Press (Implicit Difn) 4 Press . Now let’s do one on the TI-89: Find . Select and press . Calculus Tools Press (Deriv) Enter the equation. (You may have to unlock the alpha mode.) Set the order to 2.

10. Press and then to return your calculator to normal. ESC HOME p