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 transcript:

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 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

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

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