Question

Find intervals in which the function given by $f\left(x\right)=\frac{3}{10}{x}^4-\frac{4}{5}{x}^3-{3x}^2+\frac{36}{5}x+11$ is (a) strictly increasing (b) strictly decreasing.

Answer 1

$f^1\left(x\right)=\frac{6}{5}{x}^3-\frac{12}{5}{x}^2-6x+\frac{36}{5}$

$f^1\left(x\right)=\frac{6}{5}(x+2)(x-1)(x-3)$

Now, for increasing

$f^1\left(x\right)>0$

So, $xϵ(-2,1)\cup (3,\infty )$

and for decreasing,

$f^1\left(x\right)<0$

So, $xϵ(-\infty ,-2)\cup (1,3)$