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Do Now

Do Now. Which of the following statements could be true if ?. A). B). C). D). Only A and C could be true (but not simultaneously…). Implicit Differentiation. Section 3.7b. We can use Imp. Diff. with other familiar processes,

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Do Now

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  1. Do Now Which of the following statements could be true if ? A) B) C) D) Only A and C could be true (but not simultaneously…)

  2. Implicit Differentiation Section 3.7b

  3. We can use Imp. Diff. with other familiar processes, including finding tangents, normals, and/or higher- order derivatives… Find the second derivative: (when )

  4. To find the second derivative, simply differentiate again: …and substitute for y’ so that we have y’’ in terms of x and y: (when )

  5. Practice Problems Find the second derivative:

  6. Practice Problems Find the second derivative:

  7. Practice Problems Find the second derivative:

  8. Practice Problems Find the second derivative:

  9. Practice Problems Find the second derivative:

  10. Practice Problems Find the tangent and normal to the ellipse at the point (–1, 2). First, find slope: Next, evaluate slope at (–1, 2):

  11. Practice Problems Find the tangent and normal to the ellipse at the point (–1, 2). Point: Slope: Tangent Normal

  12. Practice Problems For each of the following, find the lines that are (a) tangent and (b) normal to the given curve at the given point. Normal: Tangent:

  13. Practice Problems For each of the following, find the lines that are (a) tangent and (b) normal to the given curve at the given point. Normal: Tangent:

  14. Practice Problems For each of the following, find the lines that are (a) tangent and (b) normal to the given curve at the given point. Tangent: Normal:

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