Find the intervals of increase and decrease for f(x) = x4 - 6x2. Find local maxi

Question

Find the intervals of increase and decrease for f(x) = x4 - 6x2. Find local maximum and local minimum values. Find intervals of concavity and the inflection points. Sketch the graph Repeat a similar analysis with f(x) =4x2-5/x2-1 (Find domain, asymptotes, etc). Find the absolute maximum and absolute minimum of f(x) = x/ x2+1 on the interval [0,2]. x 1

Explanation / Answer

find intervals of increase and decrease you derive the function. f(x)=x^4-6^2 f'(x)=4x^3-12x then set it equal to 0 4x^3-12x=0 4x(x^2-3)=0 x= 0, ?3, -?3 plot a line graph where'd it look like this --------(-?3)------(0)----------(?3)------- plug in points that are before and after each number to get a number ex. use -2, -1, 1, 2 f(-2)= -32+24 = -12 therefore its decreasing from (-infinity, to -?3) f(-1)= -4+12 = 8 -----> from -?3 to 0 its increasing then to find local max/min you do the second derivative test and set it equal to zero. then do as above f"(x)=12x^2-12=0 12(x^2-1)=0 x=

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