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Critical Numbers and Finding Extrema

Critical Numbers and Finding Extrema. Critical Numbers. Example 2:. Take the derivative of f(x) Set the derivative equal to zero Solve for x. * Remember to test the regions to make sure the critical numbers are valid. Example 1:.

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Critical Numbers and Finding Extrema

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  1. Critical Numbers and Finding Extrema

  2. Critical Numbers Example 2: Take the derivative of f(x) Set the derivative equal to zero Solve for x *Remember to test the regions to make sure the critical numbers are valid Example 1: 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) • Find critical numbers • Find endpoint values • Find the function values for the x values determined in step one and two • Identify extrema • Largest overall function value is the absolute max • 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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