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2.4 Rates of Change and Tangent Lines

2.4 Rates of Change and Tangent Lines. Goal: Find the average rate of change of a function over an interval. Find the slope of the curve at the indicated point. Determine whether the curve has a tangent at the indicated point. Find the equation of the tangent line and normal line. .

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2.4 Rates of Change and Tangent Lines

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  1. 2.4 Rates of Change and Tangent Lines Goal: Find the average rate of change of a function over an interval. Find the slope of the curve at the indicated point. Determine whether the curve has a tangent at the indicated point. Find the equation of the tangent line and normal line.

  2. 1. Find the average rate of change over the given intervals. • a) [-1,3] b) [-2,-1]

  3. 2.

  4. 3. Find the slope of the curve • Instantaneous rate of change

  5. Definition of a Tangent Line Use point slope to write equation of the line 1,2,3

  6. 4. Find the equation of the tangent line if it exists • when x=4 4

  7. 5. Find the equation of the tangent line if it exists • at x=0 • Hint: Find the left handed limit and the right handed limit. 5,6

  8. 6. Free Fall (m/s) • An object is dropped from a cliff 450 meters above the ground. The height above the ground after t seconds is • after falling. • Instantaneous:

  9. 7. Find the rate of change of a square with sides 4 inches The rate of change is the Area/radius Therefore

  10. Last Question!! • Find the point where there is a horizontal tangent: 7

  11. Homework • 2.4 InterActMath • Test 2 Monday

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