Question

The intervals in which the polynomial $2x^3-15x+36x+1$ is increasing be $[-\infty ,k],[m,\infty ]$ and decreasing be [k,m].Find $k+m$ ?

Answer 1

Function $f\left(x\right)$ will increase if derivative of that function is greater than $0$.

So find the interval in which the derivative of given function is greater than zero.

$6x^2-30x+36>0$ which implies $x>3$ and $x<2$.

So $m=3,k=2$, therefore $m+k=5$.