Question
Asked Oct 17, 2019
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 Let f(x)=8x^2−8x^4\. Find the open intervals on which f is increasing (decreasing). Then determine the xx-coordinates of all relative maxima (minima).

 

1.   f is increasing on the intervals  
2.   f is decreasing on the intervals  
3.   The relative maxima of f occur at x =  
4.   The relative minima of f occur at x =  
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Expert Answer

Step 1
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Given: f(x)=8x2-8r The domain of the given function is (-0, ) Obtain the derivative of f(x) as shown below f(x)16x-32x Critical point: f(x)0 16x-32x 0 16x(1-2x2)=0 x 0,x 0.707,x=-0.707

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Step 2
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Split the interval and obtain the behavior of f(x) as shown below. ox-0.707 x -0.707 -0.707<x <0 х Test point -1 -0.5 f(x) 0 0 Decreasing Behavior Increasing 0.707 < x < o 0 x 0.707 x = 0.707 х Test point f(x) 0.5 1 0 Increasing Behavior Decreasing

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