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Warm-ups

Warm-ups. 1) Find the equations of all lines tangent to y = 9 – x 2 that passes through the point (1, 12) . Warm-ups. 2) TRUE OR FALSE: If the graph of a function has a tangent line at x = a, then the graph also has a normal line at x = a. Justify your answer. Warm-ups.

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Warm-ups

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  1. Warm-ups 1) Find the equations of all lines tangent to y = 9 – x2that passes through the point (1, 12).

  2. Warm-ups 2) TRUE OR FALSE: If the graph of a function has a tangent line at x = a, then the graph also has a normal line at x = a. Justify your answer.

  3. Warm-ups MULTIPLE CHOICE: Find the average rate of change of f(x) = x2 + x over the interval [1, 3] A) -5 B) 1/5 C) ¼ D) 4 E) 5

  4. Warm-ups 4) MULTIPLE CHOICE: Which of the following is an equation of the normal to the graph of f(x) = 2/x at x = 1. A) y = ½x + 3/2 B) y = - ½x C) y = ½x + 2 D) y = -½ x + 2 E) y = 2x + 5

  5. Rates of change and Tangent lines: Applications

  6. Example: Using the function f(t) = 2t2- 1, find the following … a) The instantaneous rate of change at t = 2.

  7. Example: Using the function f(t) = 2t2- 1, find the following …

  8. Example: Find the speed of the rock that freefalls from a cliff at t = 1 sec.

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