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

this is calculus and probably involves the first derivative test

May 20, 2018

Check below

Explanation:

$f \left(x\right) = 6 {x}^{5} - 10 {x}^{3}$ , ${D}_{f} = \mathbb{R}$

We notice that $f \left(0\right) = 0$

$f ' \left(x\right) = 30 {x}^{4} - 30 {x}^{2} = 30 {x}^{2} \left({x}^{2} - 1\right)$

• $f ' \left(x\right) > 0$ $\iff$ $30 {x}^{2} \left({x}^{2} - 1\right)$

$\iff$ $x < - 1$ or $x > 1$

• $f ' \left(x\right) < 0$ $\iff$ $- 1 <$$x < 1$

Hence, $f$ is increasing in $\left(- \infty , - 1\right)$ and $\left(1 , + \infty\right)$ and decreasing in $\left(- 1 , 1\right)$

$f$ 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]}