Question

Find the intervals in which $f\left(x\right)={(x+1)}^3{(x-3)}^3$ is increasing and decreasing.

Answer 1

Let us consider the problem:-

$(x+1{)}^3(x-3{)}^3$

Therefore, there are three region to check for function's increasing or decreasing nature

$\left(-\infty ,-1\right),\left(-1,3\right),\left(3,\infty \right)$

$\left(-\infty ,-1\right)\to$ By substitute any value less than $\left(-1\right)$ greater than $\left(3\right)$ $(\to )$ increasing

$\left(3,\infty \right)\to$ we can say that function is positive $\to$ Increasing

$\left(-1,3\right)\to$ By substitute any value between $\left(-1,3\right)$

We can say that function is negative $\to$ Decreasing