Hello I need help with these problems. The direction said(adsbygoogle = window.adsbygoogle || []).push({});

a. find the intervals on which f is increasing, b. the intervals on which f is decreasing, c. the open intervals on which f is concave up, d. the open intervals on which f is concave down and e. the x-cordincates of all inflection points

1. f(x)=x^4-8x^2+16

I find a,b c and d for this function. However I have trouble finding the inflection points for this function. When you find the inflection point you suppose to set up the second derivative of the function to equal 0 but I have no idea how to solve it afterward. Is there an inflection point for this equation?

f"(x)=12x^2-16

2.f(x)=x/(x^2+2)

so f'(x)=-x^{2}+2/(x^{2}+2)^{2}

to find a,b I have to set this equal to 0 and solve it. How do I solve it? and what would be the second derivative and how do I solve it by setting it up to equal to 0 to know if it's concave up or down?

3.f(x)=x^{2}lnx

The first derivative is 2xlnx+x. How do I solve it or know what is a, b is?and the second derivative is 2lnx+3. How do I use the second derivative to solve for c,d and e?

Please help! Thank you!

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# Homework Help: Analysis of Functions I: increase, decrease, and concavity

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