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Critical Numbers and Finding Extrema. Critical Numbers Example 1: Example 2: 1.Take the derivative of f(x) 2.Set the derivative equal to zero 3.Solve.

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Presentation on theme: "Critical Numbers and Finding Extrema. Critical Numbers Example 1: Example 2: 1.Take the derivative of f(x) 2.Set the derivative equal to zero 3.Solve."— Presentation transcript:

1 Critical Numbers and Finding Extrema

2 Critical Numbers Example 1: Example 2: 1.Take the derivative of f(x) 2.Set the derivative equal to zero 3.Solve for x *Remember to test the regions to make sure the critical numbers are valid you can’t take the square root of a negative number, so the only critical number is 0

3 Finding Extrema (closed interval, continuous function) 1.Find critical numbers 2.Find endpoint values 3.Find the function values for the x values determined in step one and two 4.Identify extrema a.Largest overall function value is the absolute max b.Smallest overall function value is the absolute min

4 Finding Extrema Example Find the absolute min and max for the function on the interval [-3,5] : Absolute max is 66 and occurs at x=5 and the absolute min is -15 and occurs at x=2

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