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12.1

Parametric Equations. 12.1. Find the derivative. Parametric equations can be used to describe motion that is not a function. If f and g have derivatives at t , then the parametrized curve also has a derivative at t. The formula for finding the slope of a parametrized curve is:.

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12.1

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  1. Parametric Equations 12.1

  2. Find the derivative.

  3. Parametric equations can be used to describe motion that is not a function. If f and g have derivatives at t, then the parametrized curve also has a derivative at t.

  4. The formula for finding the slope of a parametrized curve is: This makes sense if we think about canceling dt.

  5. The formula for finding the slope of a parametrized curve is: We assume that the denominator is not zero.

  6. To find the second derivative of a parametrized curve, we find the derivative of the first derivative: • Find the first derivative (dy/dx). 2. Find the derivative of dy/dx with respect to t. 3. Divide by dx/dt.

  7. Example:

  8. Example: • Find the first derivative (dy/dx).

  9. 2. Find the derivative of dy/dx with respect to t. Quotient Rule

  10. 3. Divide by dx/dt.

  11. Find the slope of the line tangent to the point on the circle:

  12. Find the slope of the line tangent to the point on the circle: What is the equation of the line tangent to the point on the circle? Point:

  13. Determine the concavity of the cycloid on the interval This is always negative so the graph is concave down.

  14. Homework Page 535 #16-25, 27-31 all

  15. Homework Page 535 #1-15 odd, 16-31 all

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