Please help $f (x) = 6 x^{5} - 10 x^{3}$ $f(x)=6x^5-10x^3$ a. find the $x$ $x$ coordinates of all max and min points. b. State the intervals where f is increasing?

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this is calculus and probably involves the first derivative test

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Answer 1 · 2018-05-20T01:50:20

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$f (x) = 6 x^{5} - 10 x^{3}$ $f(x)=6x^5-10x^3$ , $D_f=RR$

We notice that $f(0)=0$

$f'(x)=30x^4-30x^2=30x^2(x^2-1)$

$<=>$ $x<-1$ or $x>1$

Hence, $f$ is increasing in $(-oo,-1)$ and $(1,+oo)$ and decreasing in $(-1,1)$

$f$ has global and local minimum at $x=1$ and maximum at $x=-1$

Graphical help graph{6x^5-10x^3 [-8.89, 8.9, -4.44, 4.444]}